Stefan Mehedinteanu
email: s.mehedinteanu@gmail.com

The Lensing Effect a Proof of Large Scale Entanglement in Holographic CFTs for Non-Black Holes Objects

Many experimental works at small scale (photons, electrons, etc.) try to confirm the entanglement, in this work we will show that the Einstein ring could be a such proof of entanglement but at very large scale (cosmic objects), when, due of a QCD operation (Schwinger effect) inside nucleons is infused in quantum a flux of energy (pulse) that corresponds to stress-energy tensor onto attached nucleons as of  n sheeted Riemann surfaces glued to the boundaries (CFT), there producing a strain of space -the lensing effect. This approach is tested on light lensing around objects (Earth). FIG.1 from ref [6] : (a) AdS3 space and CFT2 living on its boundary and (b) a geodesics A  as a holographic screen. With the central charge

)

Introduction

I my recent works, see in the following, I found that a Black Holes (BH) could be assimilated with space-time region created at the epoch of EWPT (more QGP), where the inside is filled with quarks open strings, which rotate in equilibrium with an accretion disk, so which don't eat nothing, it look more like SATURN planet with its rings, in rest is a imagination about being a monster! "Stefan Mehedinteanu. More On "What Would Be Inside of M87* to Explain the Event Horizon Telescope (EHT) Results ?". 2019. hal-02263360", (Online) 2349-7882" Now, we know that the light is bended by planets, stars, any structured matter objects etc. that is explained by geodesic of spacetime deformation, since the quarks are confined in thin tubes due of gluonic confinement inside nucleons, they don't radiate bit threads as in case of BH, for that we have also an explanation in entanglement theory, I will present it in this paper.

2.. Universality of Gravity from Entanglement

In the following we realize a compilation of some articles which describe the role of entanglement in the explanation of the "distance effect" mainly in the transfer of stress-energy to the boundary of the objects. Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently of the others, even when the particles are separated by a large distance-instead, a quantum state must be described for the system as a whole. According to AntiDeSitter/Conformal Field Theory (AdS/CFT) correspondence, gravitational theories on AdS3 space of radius R are dual to (1+1)D CFTs with the central charge ) (c , see Fig. 1 reproduced from ref. [START_REF] Ryu | Holographic Derivation of Entanglement Entropy from AdS/CFT[END_REF]. the Ryu-Takayanagi prescription [START_REF] Ryu | Holographic Derivation of Entanglement Entropy from AdS/CFT[END_REF] for a spherical entangling surface.

Emergence of cosmological Friedmann equations from quantum entanglement

A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF]. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy. The generalized second law (GSL) thus points to a deep link between vacuum entanglement and the Einstein equation [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF].

First approach

In [START_REF] Ge | Emergence of cosmological Friedmann equations from quantum entanglement[END_REF], [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF] is studied the deep connections between the concepts of quantum information theory and cosmology. Employing Fermi normal coordinates and conformal Fermi coordinates, we follow these works to construct a relation between Friedmann equations of Friedmann-Lemaitre-Robertson-Walker (FLRW) universe and entanglement. Fermi normal coordinates (FNC) are determined by an orthonormal reference frame  Friedmann equations are derived with the first law of entanglement under the assumption that entanglement entropy in a geodesic balls is maximized at fixed volume. More brief, we can expand the spacetime elements as

) ( i F x h g      
, so in the Fermi normal coordinates

) ( i F
x the metric becomes the following equations

  j F i F j i F x x O R g 0 0 00 1  
where ikjl F R denotes the projection of the Riemann tensor. This leads a new presentation of the FLRW metric in Fermi normal coordinates (for

1  H x   )                         j F i F j F i F ij F F ij F F F F dx dx x x x t H a K dt x t H t H ds 3 ) ( ) ) ( ) ( ( 1 2 2 2 2 2 2 2   
The FNC obtained here can also be evaluated via 00 g . In particular, the spatial components of the Ricci scalar can be easily evaluated as

        2 2 ) ( 6 F ij ij F t H a K R , 0 ,  j i
The area deficit Let us first consider the FNC system central at the geodesic O in a spacetime of dimension d. The geodesics sending out from O orthogonal to a u forms a (d-1) dimensional spacelike ball  . We assume that l is the radius of the ball. Consider a Fermi normal coordinate system based at O, with the timelike coordinate be 0 ). Note that this condition can be relaxed by considering conformal Fermi coordinates. More briefy, we can expand the spacetime elements as

) ( i F x h g      
on  is given in [START_REF] Ge | Emergence of cosmological Friedmann equations from quantum entanglement[END_REF]. The volume element of  to the second order of the FNC coordinates is given by

x d h dV d 1  
; h the spatial metric ij h on  is expressed in terms of ijkl R -the spatial components of the spacetime Riemann tensor evaluated at o. Then, the area variation at fixed volume satisfies [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF]

      ) 1 ( 2 2 2 , d l A d d l V R  (a) 00 2 2 1 G R    ;  -scalar Ricci curvature
The area deficit can thus also be expressed as

00 2 2 ) 1 ( G d l A d d V      
Then, using the Einstein equation

ab ab GT G  8 
, we see that the area deficit is proportional to the energy density,

00 2 2 ) 1 ( 8 T d l G A d d V        (a')
For the Friedmann-Robertson-Walker metric, the spatial Ricci scalar is given by ) ( 6 and the conformal isometry for the Minkowski line element were discussed in great detail in [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF]. It was derived that the unique conformal isometry preserving the diamond with spherical symmetry is generated by the Killing vector [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF]  

r t rt t r l l       2 ) ( 2 1 2 2 2



For the at FLRW geometry with line elements

2 2 2 2 ) ( x d t a dt ds   
, we can define a conformal time coordinate

     t t a t d ) (



For general FLRW metric 2 ds at arbitrary space curvature, it takes the form

2 2 2 2       d r d d ds   with null coordinates              dr kr t a dt d 2 1 ) (               dr kr t a dt d 2 1
) (



The conformal Killing vector then takes the form

                                ) cos (cos cos cos sin 1 a k a l k a k a l k a kl k a
As k = 0, the conformal Killing vector field yields a new form

                    2 2 2 2 2 1 l l l
For non-conformal matter systems, the entanglement entropy in the causal diamond ) ( D is consisted of two contributions, the UV part and the IR part. If we consider the variation of the geometry and the state of the quantum fields, the total variation of the entanglement entropy is contributed from both the area change induced by

IR IR UV total S dA S S S          (b) If G  4 1  
, coincides with the variation of Bekenstein's generalized entropy, here interpreted as simply the total entropy in the diamond [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF]. Jacobson proposed the maximal vacuum entanglement hypothesis (MVEH) in [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF]: when the geometry and quantum fields are simultaneously varied from maximal symmetry, the entanglement entropy in a small geodesic ball is maximal at fixed volume. The MVEH indicates that the above total entropy variation at fixed volume is vanishing at first order. That is to say 0  total S  They in [START_REF] Ge | Emergence of cosmological Friedmann equations from quantum entanglement[END_REF] proceed to derive the Friedmann equations under the MVEH first in the Fermi normal coordinates system and then we turn to conformal normal coordinate

Entanglement and Friedmann equations

In this section, we will make use of the first law of the entanglement

      H S
and derive the Friedmann equation of the universe. Now let us assume the quantum states enclosed by the causal diamond are in thermodynamical equilibrium. Above, it is derived the area variation at fixed volume. This reminds us to take into account the minimal Helmholtz free energy TS E F   at fixed volume in the ordinary thermodynamic system in equilibrium. The vacuum state of the Quantuum Field Theory (QFT) restricted to the diamond can be expressed as a thermal density matrix

T K e Z    1



; where K is related to the modular Hamiltonian and T the temperature. Note that for infinite diamond that overlaps with the Rindler wedge in Minskowski space, T is the Unruh temperature

B ck a  2 
or Hawking temperature when the acceleration g a  , see ref. [19, 20] cited in [START_REF] Ge | Emergence of cosmological Friedmann equations from quantum entanglement[END_REF]. The modular free energy is given by

TS K F K     

denotes quantum expectation value of the modular Hamiltonian and S represents the von Neumann entropy

] [ ln 1    JK Tr k S B  
in the causal diamond,  -density matrix as resulted from Gibbs entropy

i i B p p k S ln    ; W p i 1 
the probability of a microstate; W -the number of microstates, and the Boltzmann eq. ) ln(W k S B 

. The variation K F  must vanish due to the minimal Helmholtz free energy principle. This in turn leads to the minimal Helmholtz free energy principle. This in turn leads to

   K S IR     2 (c)
This can be interpreted as the usual Clausius relation for a thermal state. The connections between K and  H were discussed in great detail in [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF].

In general K in  above, is not a local operator, and does not generate a geometric flow. For a CFT, however, K is equal to  H , the Hamiltonian generating the flow of the conformal boost Killing vector above. (This result is conformally related to the better-known version that holds for any Poincaré invariant QFT restricted to the Rindler wedge.) That is,  H is given by the integral can be treated as constant, and using the Killing field above is find

        00 2 2 1 T d l H d d    (c')
If  were a Killing vector,  H would vanish for all fields invariant under the Killing flow. For matter treated as a fluid, it would not vanish, because the fluid potentials do not share the symmetry of the metric. If  is only a conformal Killing vector,  H does not vanish. In general it receives contributions both from matter and from the gravitational field. If the matter field is not conformal, K is not given by above  H , and we cannot directly use

        dQ H
from appendix (D2) of [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF] , see below. However, suppose that the matter is described by a QFT with a UV fixed point, so it is asymptotically conformal at short distances, and that, in addition to

excitation L l 
, the diamond is much smaller than any length scale in the QFT, QFT L l  Then we conjecture-and we shall assume-that  K  has the form of that from the Appendix (D2) with an additional term X  that is a spacetime scalar,   -sphere, X was first introduced in [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF], and see also the comment in [7f] about X  , see below. That it was developed on the base of the next section as from [7d], which could be some scalar operator in the QFT. In what follows we only consider a special case in which d = 4.

X T d l K d d             00 2 2 1 (d)
First law of causal diamond mechanics [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF] Here, if  is only a conformal Killing vector,  H does not vanish. In general it receives contributions both from matter and from the gravitational field. If the theory is general relativity, and the background solution is Minkowski spacetime, then the gravitational field contribution to  H turns out to be

Gl V d H     8 ) 2 (   
(see [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF], [START_REF] Hollands | Stability of Black Holes and Black Branes[END_REF]). Since, following [START_REF] Hollands | Stability of Black Holes and Black Branes[END_REF] , the variation of the Lagrangian (L) for vacuum general relativity can be written as d')

         g d d g d g d d g E g L d d     ; ) ( ) ( (
where E = 0 are the field equations and  corresponds to the boundary term that would arise if the variation were performed under an integral sign, namely, see eq.( 17) from [START_REF] Hollands | Stability of Black Holes and Black Branes[END_REF],

, 16

1 1 1 1 ... 1 ...    d d a ca c a a v    where           bd c bc d bd ac a g d d g d d g g v  
The symplectic current (D -1)-form ω is defined as

                                      g g g g g g g 1 2 2 1 2 1 ; ; ; ;         
If both perturbations satisfy the linearized equations of motion, then it follows by taking a second, antisymmetrized variation of (d')

that  is closed, 0   d Concretely, ω(g; γ1, γ2) is given by 1 1 1 1 ... ... 16 1    D D a ca c a a w   
The symplectic form of the linearized Hamiltonian equations of motion

    ) , ; ( ) , ; ( 2 1 2 1      g g W
is obtained by integrating  over a Cauchy surface  , or as in [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF] 

   a a d g w G H ) , , ( 16
1 2 1     
, where finally as in [START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF] h

h l d w t  2 2   
, inserting this we have

Gl V d H     8 ) 2 (   
; where,  is the surface gravity

] [ 8 1 3   s GM c   ,
for Planck particle mass results

1 42 10 6 . 1    s  .
The surface gravity 1   is unity for the chosen conformal Killing field, so this yields the result claimed above. Here, is used the Lie derivative of the Minkowski metric along  is

ab ab l t    ) 2 (   

When combined with the area variation term

G A   8  this yields G   8  times the area variation V A
 at fixed volume, [Eq. (a), above]. Moreover, the conformal boost energy of the matter integrated over  is given by the right hand side of [Eq. (a'), above], when 00 T is constant. In this way we see that

        dQ H
recovers the statement of [Eq. (a'), above], that addition of matter energy to the diamond decreases the area of the boundary at fixed volume, where,  H is the Hamiltonian generating evolution along the flow of  (constructed from the symplectic form evaluated on the Lie derivative of the fields along

 ),  Q is the associated Noether charge ) 2 (  d
-form, and the variation is to any neighboring solution [START_REF] Iyer | Some properties of Noether charge and a proposal for dynamical black hole entropy[END_REF]. Now suppose that the quantum fields in the causal diamond is in thermodynamic equilibrium and are dominated by the vacuum state.

The total entanglement entropy variation at fixed volume is zero. That is, from (b), (c), (d) and (a), we obtain

      K S S IR UV      2 This leads to   X T          00 2 2  and then   X T a K H                00 2 2 2 3  (e)
We can assume 0

 X  in what follows, G  4 1   .
To the first order, we assume the universe is not empty but dominated by some matter and energy. We choose to model the matter and energy in the universe by a perfect fluid. The energy-momentum tensor for a perfect fluid can be written

        pg U U p T     
where  and p are the energy density and pressure (respectively) as measured in the rest Fermi frame, and  U is the four-velocity of the fluid. The four-velocity is given by )

0 , 0 , 0 , 1 (   U
. The energy-momentum tensor can be simply expressed as

) , , , ( p p p diag T        
We can then recast (e) into the standard Friedmann equation

  3 8 2 2 G a K H   (f)
But , that is true only for objects like BHs, and as I will show below it is not the case for structured matter of planets, stars etc. as constituted from nucleons when the stress-energy have discrete values in the bulk, see below.

Together with the continuity equation of the perfect fluid

) ( 3 P p H     
we obtain another Friedmann equation

) ( 4 2 P G a K H        (g)
where the dot denotes derivative with respect to F t . Thus, are obtained the Friedmann equations for the FLRW universe by applying the first law of entanglement. In this sense, the emergences of the Friedmann equations can be considered as a consequence of the change in entanglement A S  caused by matter

  A H 
. The validity of the derivation is restricted to a small geodesic ball region with radius much smaller than the horizon. To overcome this limitation, in [START_REF] Ge | Emergence of cosmological Friedmann equations from quantum entanglement[END_REF] is explored the conformal Fermi coordinates, which is a generalization of FNC. The authors in ref. [START_REF] Hinterbichler | Symmetron Fields: Screening Long-Range Forces Through Local Symmetry Restoration[END_REF] cited in [START_REF] Faulkner | Gravitation from entanglement in holographic CFTs[END_REF] introduced the conformal Fermi coordinates (CFC) in order to cosmological application. Compared to the FNC, the CFC are valid outside the horizon. Similar to FNC, the CFC are constructed nearby a timelike central geodesic. In the CFC frame, the lowest order CFC metric is at FLRW spacetime. Thus are obtained the Friedmann equations (f), (g) in the CFC frame for flat universe, but in case of 0  K .

An approach for structured matter

In the following we use and follow the model described in [START_REF] Ryu | Holographic Derivation of Entanglement Entropy from AdS/CFT[END_REF], [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF].

For theories with entanglement the entropy is computed by the Ryu-Takayanagi formula as  plays the role of a holographic screen for an observer who is only accessible to the subsystem A. They show explicitly this relation in the lowest dimensional case d = 1, where A  is given by a geodesic line in AdS3.

The different approach [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF] For the case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c , in [11c] is re-derived the result l c S A log ) 3 (  of Holzhey et al. [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF] when A is a finite interval of length l in an infinite system, and extend it to many other cases: finite systems, finite temperatures, and when A consists of an arbitrary number of disjoint intervals. For such a system away from its critical point, when the correlation length  (inverse mass) is large but finite, is shown that

 log ) 6 (c A S A 
, where A is the number of boundary points of A [11c]. Thus, in the case of a massive 1+1-dimensional field theory it results a c S  log ) 6 (  from completely general properties of the stress tensor in the relevant geometry, a is the lattice spacing. This is then verified for a free bosonic massive field. So, is rederived

    ln 6 c c S
from [START_REF] Ryu | Holographic Derivation of Entanglement Entropy from AdS/CFT[END_REF], [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF]. in a manner which stresses how the entropy arises through coarse graining in real space, without explicit use of mode expansions or modular invariance. The calculation follows ideas of Cardy [START_REF] Hollands | Stability of Black Holes and Black Branes[END_REF] cited in [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF].

Path integral formula for the Entanglement Entropy

Consider a lattice quantum theory in one space and one time dimension [11b]. The lattice spacing is a , and the lattice sites are labelled by a discrete variable x . The domain of x can be finite, i.e. some interval of length L, semi-infinite, or infinite. Time is considered to be continuous. A complete set of local commuting observables will be denoted by  

) ( ˆx



, and their eigenvalues and corresponding eigenstates by  

) ( ˆx  and   ) (x x  
respectively. For a bosonic lattice field theory, these will be the fundamental bosonic fields of the theory; for a spin model some particular component of the local spin. The dynamics of the theory is described by a timeevolution operator  ˆ. The density matrix  in a thermal state at inverse temperature  is

           ) ( ) ( ) ( ) ( ) ( 1                x e x Z x x H        where H Tre Z ) (    
is the partition function This may be expressed in the standard way as a (euclidean) path integral: , and is found by setting {φ(x)′′} = {φ(x)′} and integrating over these variables. This has the effect of sewing together the edges along τ = 0 and τ = β to form a cylinder of circumference β. Let A be a subsystem consisting of the points x in the disjoint intervals ) , ( ),..., , (

                x S x E e x x x x x d Z ) ) ( ) , ( ( ) ) ( ) 0 , ( ( ) , ( 1           (2.
1 1 N N v u v u
. An expression for the reduced density matrix A  may be found by sewing together only those points x which are not in A. This will leave open cuts, one for each interval ) , (

j j v u
, along the line τ = 0. See figure 1 from [START_REF] Calabrese | Entanglement entropy and conformal field theory[END_REF] for a pictorial representation of this. The normalization factor of the partition function ensures that 1  

Tr

, and is found by setting {φ(x)′′} = {φ(x)′} and integrating over these variables. This has the effect of sewing together the edges along τ = 0 and τ = β to form a cylinder of circumference β. We may then compute

n A
Tr , for any positive integer n , by making n copies of the above, labelled by an integer k with 1 ≤ k ≤ n, and sewing them together cyclically along the cuts so that

) ( ) (      k k x x   and ) ) ( ) ( ( 1     x x and n  
for all x ∈ A. Let us denote the path integral on this n -sheeted structure by

) ( A Z n . n n n A Z A Z Tr ) (   (2.2) Now, since      n n A

Tr

, where λ are the eigenvalues of A  (which lie in [0, 1),) and since

1  A Tr
, it follows that the left hand side is absolutely convergent and therefore analytic for all Re n > 1. The derivative wrt n therefore also exists and is analytic in the region. Moreover, if the entropy

       log A
is finite, the limit as n → 1+ of the first derivative converges to this value. They conclude that the right hand side of (2.2) above has a unique analytic continuation to Re n > 1 and that its first derivative at n = 1 gives the required entropy:

n n n n n A A n n A A n A A n A Z A Z n tr n Tr n n tr S ) ( lim log 1 1 lim 1 1 1 1                      
as the eq. from [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF] if we taking the trace, respectively,

) ( ln ) 1 ( ) 1 ( ) ( ) ( 1 1 n Z dn d n Z n Z dn d S n n n       (2.2')
Figure 2 from [START_REF] Calabrese | Entanglement entropy and conformal field theory[END_REF]. A representation of the Riemann surface 1 , 3

 .

Path integral formulation and Riemann surfaces

So far, everything has been for a discrete space domain. We now discuss the continuum limit, in which a → 0 keeping all other lengths fixed [START_REF] Calabrese | Entanglement entropy and conformal field theory[END_REF]. The points x then assume real values, and the path integral is over fields φ(x, τ) on an n-sheeted Riemann surface, with branch points at j u and j v . In this limit, SE is supposed to go over into the Euclidean action for a quantum field theory.

We indicate these n-sheeted surfaces with

N n,



and they are fully defined by the 2N branch points j u and j v . Whenever the value of n and N is not important, we will simply indicate the surface with  .

In the simplest instances it is possible to directly calculate the partition function on a n-sheeted Riemann surface, but in most of the cases this is very difficult. However, the surface we are dealing with has curvature zero everywhere except at a finite number of points (i.e. the boundaries between A and B j u and j v above). Since the lagrangian density does not depend explicitly on the Riemann surface  as a consequence of its locality, it is expected that the partition function can be expressed as an object calculated from a model on the complex plane C, where the structure of the Riemann surface is implemented through appropriate boundary conditions around the points with non-zero curvature. Consider for instance the simple Riemann surface , τ = 0. We expect that the associated partition function in a theory defined on the complex plane z = x + iτ can be written in terms of certain "fields" at

         ) , ]( [ exp ] [     x L dxd d Z
essentially defines these fields, i.e. it gives their correlation functions, up to a normalization independent of their positions. However in the model on the complex plane, this definition makes them non-local (see for a complete discussion [START_REF] Cardy | Form factors of branch-point twist fields in quantum integrable models and entanglement entropy[END_REF]). Locality is at the basis of most of the results in field theory, so it is important to recover it. The solution to the problem consists in moving the complicated topology of the world-sheet  (i.e. the space where the coordinates x, τ live) to the target space (i.e. the space where the fields live). Let us consider a model formed by n independent copies of the original model. (Note that n is the number of Riemann sheets necessary to describe the Riemann surface by coordinates on the plane.) The partition function above can be re-written as the path integral on the complex plane

         1 1 )) , ]( [ ... ) , ]( [ ( exp ] ... [ 1 1 v Cu C n n x L x L dxd d d Z       
where with  1 1 v Cu we indicated the restricted path integral with conditions

) 0 , ( ) 0 , ( 1     x x i i   , n i v u x ,..., 1 ], , [ 1 1
  where we identify n + i ≡ i. The lagrangian density of the multi-copy model is  as in [11c], also see below. (see Fig. 2 for the case T ). More precisely, we have as from [START_REF] Cardy | Form factors of branch-point twist fields in quantum integrable models and entanglement entropy[END_REF], where L coming from the th i copy of L . The generalization to Riemann surfaces with more branch points is straightforward, but will not be needed here. The conformal dimension of branch-point twist fields was calculated in [START_REF] Calabrese | Entanglement entropy and quantum field theory[END_REF]. Consider the model L to be a conformal field theory (CFT). Then also

) , ]( [ ... ) , ]( [ ) , ]( ,..., [ 1 1 )
(        x L x L x L n n n    so
1 1 a u  , 2 1 a v  2 , 2 1 2 , 1 , ) 0 , ( ) 0 , ( ) , (  
) (n L is a CFT. There are n fields ) (z T j in ) (n
L that correspond to the stress-energy tensors of the n copies of L , and in particular the sum

   1 ) ( ) ( ) ( j j n z T z T is the stress-energy tensor of ) (n L . The central charge of ) (n L is nc if c is that of L . Consider the stress-energy tensor ) (w T in L .
We can evaluate the one-point function

          
, see below the continuation.

ENTANGLEMENT ENTROPY IN 2D CONFORMAL FIELD THEORY

Now specialize the discussion of the previous section to the case when the field theory is relativistic and massless, i.e. a conformal field theory (CFT), with central charge c, and initially consider the case of zero temperature [11c]. We show that in this case the ratio of partition functions in (2.2) is the same as the correlation function arising from the insertion of primary scaling operators ) (

j n u  and ) ( j n v   , with scaling dimensions ) 1 1 )( 12 ( 2 2 n c X n n    
, into each of the n (disconnected) sheets. Moreover, this 2N-point correlation function is computable from the Ward identities of CFT.

Single interval

They first consider the case N = 1 and no boundaries, that is the case considered by Holzhey et al. [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF] of a single interval of length ℓ in an infinitely long 1d quantum system, at zero temperature. The conformal mapping w → ζ = (w-u)/(w-v) maps the branch points to (0,∞). This is then uniformised by the mapping

n n v w u w z 1 1 )) ( ) ( (       
. This maps the whole of the n-sheeted Riemann surface n  to the z-plane C. Now consider the holomorphic component of the stress tensor T(w). This is related to the transformed stress tensor T(z) by [START_REF] Belavin | Infinite conformal symmetry in two-dimensional quantum field theory[END_REF].

} , { 12 ) ( ) ( ) ( 2 v z c z T dw dz w T   , (2.3)
where {z,w} is the Schwartzian derivative

2 2 ) 2 3 ( z z z z        
. In particular, taking the expectation value of this, and using 0 ) (  C z T by translational and rotational invariance, we find

2 2 2 2 ) ( ) ( ) ( 24 ) 1 ( 1 ( } , { 12 ) ( v w u w u n c w z c w T n        (2.4)
This is to be compared with the standard form [START_REF] Belavin | Infinite conformal symmetry in two-dimensional quantum field theory[END_REF] of the correlator of T with two primary Operators

) (u n  and ) (v n  
which have the same complex scaling dimensions

) ) 1 ( 1 )( 24 ( 2 n c n n      n n u v u v v w u w v u w T n C n n             2 2 2 2 2 ) ( ) ( ) ( ) ( ) ( ) ( ) ( (2.5)
where

n   are normalized so that n n u v v u C n n         2 2 ) ( ) ( . Eq. (2.5) is equivalent to the conformal Ward identity [22] C n n n n C n n v u v v w u u w v w u w v u w T ) ( ) ( 1 1 ) ( ) ( ) ( ) ( ) ( 2 2                             (2.6)
In writing the above, we are assuming that w is a complex coordinate on a single sheet C, which is now decoupled from the others. We have therefore shown that

C n n C n n S S v u v u w T e d e w T d w T n E n E n ) ( ) ( ) ( ) ( ) ( ] [ ) ( ] [ ) ( ) ( ) (                  (2.7)
Now consider the effect of an infinitesimal conformal transformation w → w′ = w +α(w) of C which act identically on all the sheets of n  . The effect of this is to insert a factor

w d w T w i dw w T w i C C    ) ( ) ( 2 1 ) ( ) ( 2 1     (2.8)
into the path integral, where the contour C encircles the points u and v. The insertion of T(w) is given by (2.5). Since this is to be inserted on each sheet, the right hand side gets multiplied by a factor n . Since the Ward identity (2.4) determines all the properties under conformal transformations, we conclude that the renormalized

n A n n Tr Z A Z   ) (
behaves (apart from a possible overall constant) under scale and conformal transformations identically to the nth power of two-point function of a primary operator

n  with ) ) 1 ( 1 )( 24 ( 2 n c n n     
. In particular, this means that

) 1 )( 6 ( ) ) ( ( n n c n n A a u v c Tr      (2.9)
where the exponent is just

n n 4
. The power of a (corresponding to the renormalization constant Z) has been inserted so as the make the final result dimensionless, as it should be. The constants n c are not determined by this method. However 1 c must be unity. Applying the formula (2.2') to (2.9) by differentiating with respect to n and setting 1  n , we recover the result of Holzhey et al. [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF]

) 0 2 )( 6 ( 1 log ) )( 1 )( 6 ( ) 1 ( 1 1 ) 1 )( 6 ( 0 ) 1 )( 6 ( 1                                    
,where, a is the UV cut off (or lattice spacing) and we set

u v l  
, and the central charge is

) 3 ( 2 3 N G c   .
In the following we use the w coordinates as in [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF], where the system is represented by an annulus restricted to the lower halfplane. The positive real axis is the subsystem where observations are made, and the negative real axis is the rest of the universe. Forming the density matrix of the accessible subsystem we trace over variables on the negative real axis. Then the density matrix is given by a functional integral over fields over the whole annulus, with the indices X and X  of

X X 
 specifying fields on the lower and upper side of the positive real axis. As before we use the replica trick as in (2.2')) above

) ( ln ) 1 ( 1 n Z dn d n S n   where n tr n Z   ) (
is the partition function of an annulus covered n times. Extending n analytically to be slightly less than 1, we can interpret By dimensional analysis Z ln depends only on the ratio of the two radii, so we can choose to rescale only the outer radius twice as much and keep the inner one fixed. This is implemented by the rescaling

    x x x ) 2 1 (    
, in the limit where not only  but also 1 R is treated as small, i.e. we squeeze the inner boundary to a conical singularity. Using conformal invariance of the path integral measure and the definition of the energy momentum tensor as the generator of coordinate transformations it is easy to show [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF]  

         r d T r d x x T Z d 2 2 ' 2 1 ln          With     we find              r d T dn d n n Z dn d n S n n 2 1 1 1 ) 1 ( ln ) ( ln ) 1 ( ln      (2.10)
We find it illuminating to proceed slightly differently, writing

                   . . ) ( 2 2 c h dw w T w i dS T x r d T x x r d T          (2.11)
, where were introduced complex coordinates. Performing the surface integral we are to integrate over the outer surface only. The expectation value of ) (w T on a cone with angular circumference n  2 is easily found by mapping to the cone with 1  n which is simply a disc. We map n y w  and impose 0 ) (    y T on the disc. This is appropriate to our problem, since the primary object of study is the geometric entropy relative to the ground state on the disc. Using the standard transformation formula for a conformal field theory with central charge c , [START_REF] Holzhey | Geometric and Renormalized Entropy in Conformal Field Theory[END_REF], [11(a,b,c)], see eq. (2.12) from [START_REF] Belavin | Infinite conformal symmetry in two-dimensional quantum field theory[END_REF] );

S c y f T w y w T y     2 2 ) ( ) ( ( 12 )) ( ( ) ( ) ( 2 w
( y y y y w S y          2 3 )
(2.12) they find

2 2 1 ) 1 1 ( 24 ) ( w n c w T    
Inserting this in (2.11) , we find

n n c c r d T    2 ) 1 1 ( 24 2 2       (2.13) which we insert in (2.10) to find ) 2 ( 12 ) 1 ( 12 0 )) 1 ( 12 ( ) ( ) 1 12 ( 2 2
                                              6 ln c c S      By integrating this we recover     ln 6 c c S
Notice that in this procedure a finite  -independent term cannot be excluded. In this derivation the conformal anomaly plays a crucial role. Formally, and classically, the trace of the energymomentum tensor vanishes as a consequence of conformal invariance; but the necessity of regulating the quantum theory brings in the correction term c .

Another Approach: Entanglement Entropy from Weyl Anomaly

Central charges in CFTs can be defined from the Weyl anomaly (or conformal anomaly)     T [6]. Define the energy-momentum tensor  T in terms of the functional derivative of the (quantum corrected) action S with respect to the metric  g .

We can compute

n n n A A Z Z tr ) ( 1   (k)
from the partition function n Z on the n-sheeted d + 1 dimensional manifold n M as in the 2D case [START_REF] Ryu | Holographic Derivation of Entanglement Entropy from AdS/CFT[END_REF], and [11c]. Define the energy-momentum tensor  T in terms of the functional derivative of the (quantum corrected) action S with respect to the metric  g

     S g T 4 
In 2D CFTs, the Weyl anomaly is given by the well-known formula

     12 c T   (l)
where R is the scalar curvature. We can regard this as a definition of the central charge c in 2D CFTs.

Where

l is the length of the subsystem A . We thus reproduce the known result below.

a l c S A log 3  (r)
where a is the UV cut off (or lattice spacing) and we set

u v l  
. When we are away from a critical point, the logarithmic scaling law Eq. (r) does not persist for

  l
, where  is the correlation length (inverse of the mass gap). For large

) (   l
, the entanglement entropy saturates to a finite value [START_REF] Ryu | Holographic Derivation of Entanglement Entropy from AdS/CFT[END_REF], [11c].

a c S A  log 6   (s)
where A is the number of boundary points ) (n that separate A from its complement. Thus, unlike critical (1+1)D systems, the area law holds for the massive case.

To compute the entanglement entropy, we first consider the partition function n Z on the 1  d dimensional n -sheeted manifold n M . Then we find the trace of n  reduced to the subsystem A is given by the formula (k). The entanglement entropy can be found by taking the derivative of n with the 1  n limit. If we define the length scale of the manifold A by l , then the scaling of l is related to the Weyl scaling [START_REF] Ryu | Holographic Derivation of Entanglement Entropy from AdS/CFT[END_REF]. They should be the same at least in the 1  n limit. In this way we find similarly with (2.1)

    1 ) ( 2 ) ( 2
1 log log ) ( ) ( 2 log 1 1 1 1 M d M d n d n A A x T g x d n x T g x d Z n Z x x xg d tr dl d l n                       (m) When we consider a CFT on 1    d M
, the second term (i.e. integral on

1 1     d M M
) become obviously vanishing. Below we omit writing the second term explicitly just to make the appearance of expressions simple even if M is a curved manifold. Then the entanglement entropy satisfies

  n M d n n A A n A x T g x d n tr n dl d l S dl d l                  ) ( 2 1 log 1 1 1 lim lim     (n)
Eq. (m) can be used to relate the entanglement entropy and central charge in a direct fashion. It is also possible to derive (s) from (n) We will call eq. (u) as Ryu-Takayanagi formula eq. (4.26) from [ [START_REF] Ryu | Holographic Derivation of Entanglement Entropy from AdS/CFT[END_REF] Similarly, but to account for the above "boundary points", we have as follow: we accounts of stress tensors integral by multiplying by a factor 

2 1
corresponding to the conventional normalization of the stress tensor [11c ],

  1 1 6 2 1 2 2           n n c T g x d      , or,       1 2 . 6 2 3 2 2 n G T g x d    ; or,    1 2 2 3 2 2 2 2 n G H T g x d           (u') Finally,    00 T
we have from eq. (u'):

] [ 3 8 2 2   s H n G bulk   (v)
, where

et RiemannShe n n 
, and

3 2 C j n bulk c T n n t RiemanShee      ; Tensor energy stress nucleon V T j        
; see below.

Magnetic field generation at the Confinement mechanism

At present, we have no analytic proof of the existence of the condensate of abelian magnetic monopoles in gluodynamics and in chromodynamics. However, there are two large gaps between QCD and the dual-superconductor picture [START_REF] Grasso | Potential s in the Early Universe[END_REF].

1. The dual-superconductor picture is based on the Abelian gauge theory subject to the Maxwell type equations, while QCD is a non-Abelian gauge theory.

2. The dual-superconductor picture requires color-magnetic monopole condensation as the key concept, while QCD does not have such a monopole as the elementary degrees of freedom.

In [START_REF] Suzuki | The dual Meissner effect in SU(2) Landau gauge[END_REF] is found another confinement mechanism. In this note, where is sown that the dual Meissner effect in an Abelian sense works good even when monopoles do not exist, performing Monte-Carlo simulations of quenched SU(2) QCD with Landau gauge fixing. Instead of monopoles, time-dependent Abelian magnetic fields regarded as magnetic displacement currents are squeezing Abelian electric fields. The dual Meissner effect leads us to the dual London equation and the mass generation of the Abelian electric fields which suggests the existence of a dimension 2 gluon condensate. The present numerical results, hence, suggest the Abelian dual Meissner effect is the real universal mechanism of color confinement which has been sought for many years. Moreover the relation of the Abelian dual Meissner effect with the dimension 2 gluon condensate sheds new light on the importance of the gluon condensate, cited [START_REF] Hollands | Stability of Black Holes and Black Branes[END_REF][START_REF] Iyer | Some properties of Noether charge and a proposal for dynamical black hole entropy[END_REF][START_REF] Hotta | Quantum Energy Teleportation: An Introductory Review[END_REF][START_REF] Guth | [END_REF][START_REF] Hinterbichler | Symmetron Fields: Screening Long-Range Forces Through Local Symmetry Restoration[END_REF]. Hence, the Abelian fields satisfy kinematically the simple Abelian Bianchi identity

a A a A B E    4     0    a A B   (15)
The dual Meissner effect says that the squeezing of the electric flux occurs due to cancellation of the Coulombic electric fields and those from solenoidal magnetic currents. Now what happens in a smooth gauge like the Landau gauge where monopoles do not exist? From Eq.( 15), only

A B  4 
regarded as a magnetic displacement current could play the role of the solenoidal current. It is very interesting to see Fig. 4 from [START_REF] Suzuki | The dual Meissner effect in SU(2) Landau gauge[END_REF], in which this happens actually in Landau gauge. Note that the solenoidal current has a direction squeezing the Coulombic electric field. Let us see also the detailed distributions shown in Fig. 5 In comparison, we show the case of MA gauge also in Fig. 5 of [START_REF] Suzuki | The dual Meissner effect in SU(2) Landau gauge[END_REF]. Now they have shown that the magnetic displacement currents are important in the dual Meissner effect when there are no monopoles. Then how can we understand the origin of the dualMeissner effect without monopoles?. The Abelian dualMeissner effect indicates the massiveness of the Abelian electric field as an asymptotic field.

DIMENSION 2 GLUON CONDENSATE

Now in [START_REF] Suzuki | The dual Meissner effect in SU(2) Landau gauge[END_REF] is shown that the magnetic displacement currents are important in the dual Meissner effect when there are no monopoles. Then how can we understand the origin of the dualMeissner effect without monopoles? The Abelian dualMeissner effect indicates the massiveness of the Abelian electric field as an asymptotic field:

0 ) ( 2 2    A E m   (16)
This leads us to a dual London equation which is a key to the dual Meissner effect. Let us evaluate the curl of the magnetic displacement current. Using Eq.( 15), we get 16), we get the dual London equation:

A A A E E B       2 4 ) (          From Eq.(
A A E m B    ) ( 2 2 4 4       (17)
Neglecting gauge-fixing and Fadeev-Popov terms, we have equations of motion 0 

F F g F D      2 ) ( 2  Notice ) ) ( ( ) ( ) ( 2 2 2 2 c ab b a c acb ab ab A A A g A g D                 Hence if 0 2  v A A ab b a     
we see asymptotically that the electric fields become massive 0

) ( 2 2    a k E m  with 2 2 2 8 v g m 
as in [START_REF] Arriola | Landau-gauge condensates from the quark propagator on the lattice[END_REF]. Now the Abelian electric field is also massive asymptotically 0 ) (

From eq. (u') above we have an expression in terms of glued Riemann sheets n , that results from eq. ( 20)

   1 2 2 3 2 2 2 2 n G H T g x d             1 4 3 2 3 2 3 G c H c       or   1 8 3 3 2 3 G c H c      or, ] [ 3 2 2 2 3     s H l c P  , or, ] [ 1 3 2 2 2 2 3     m H c l c P   (20)
] [ 1878 m H 
, which corresponds with the above value of ] [ 1740 m H  . In the case of a homogeneous potential directed along the z-axis [START_REF] Grasso | Potential s in the Early Universe[END_REF] eq. (2.2), the Einstein stress-energy tensor is:

   8 2 2 0 33 22 11 00 B c T T T T       ; 0 0  i T
, where ] [

3 m J B  -the magnetic energy density. ] [ 8 2 2 0 J V V B c V vol vol        , 3 8 ) 4 ( 2 C C c C vol V      
, at Compton length equally with the penetration length

   C , that results 3 0 2 ) ( ) (   e C V E   With gluons V   as above is obtained c E B q q  . ] [ 8 2 2 0 J m V V B c V A vol B vol          ,
Now, the rate per unit volume of quarks pair creation is given by using the Schwinger effect R inside the nucleon or EW bubbles, when this electric field E is induced by ; the mass of quarks.

The strain at Earth surface Strain Model

From [START_REF] Ford | CLASSICAL SCALAR FIELDS AND THE GENERALIZED SECOND LAW[END_REF] we have:

kv e 1     ; M 4 1    ;    r t v ; r M C 2 1  ; and     dr C r 1 ; 2 , 2 r M C
r  We will assume that ) (v T vv represents ingoing radiation which changes the black hole's mass by only a small fractional amount, M M  

. We can then take κ to be constant to lowest order. If we change the independent variable from λ to v = t + r * , then ; if we have the generation eq. ( 22) ,

Conclusions

In this work are confirmed the following models: -author' model of electromagnetic fields in nucleon, -the origin of the gravitational potential, -the Schwinger effect to create particles inside nucleons, -the holographic derivation of entanglement for structured matter objects, -the origin of the deformation of the horizon for structured matter objects, -the lensing effect due of magnetic flux passing the hologram-CFT.

"

  Stefan Mehedinteanu (Issue 11), The Entanglement in Holographic CFTsan Alternative Explanation of the Binary Black Hole Merger (LIGO) Experiment, International Journal of Advanced Research in Physical Science (IJARPS) Volume 5, Issue 11, 2018, PP 31-42 ISSN No.

e

  is the timelike unit vector that is 3 tangent to the central geodesic O. The point    F x P is found by first following O for a proper time  and following a certain orthogonal geodesic at a proper distance  .

F.

  Assume the radius of the ball is much smaller than the local curvature length (i.e.

  The past and future development of the region enclosed by a diamond is the domain of dependence of a spherical region and the space of all ) 2 (  d -spheres is the same as the space of all causal diamonds.See FIG.1from[START_REF] Jacobson | Entanglement equilibrium and the Einstein equation[END_REF]. Causal diamond, in a maximally symmetric spacetime, for a geodesic ball  of radius l with center O and boundary   . The dashed curves are flow lines of  , the conformal Killing vector field, whose flow preserves the diamond and which vanishes at the top and bottom vertices and on   . The vectors show  at four points of  . Also, see the correspondence Figure from[START_REF] Faulkner | Gravitation from entanglement in holographic CFTs[END_REF].

Figure 1 .

 1 Figure 1. from [7] Causal development D (left) of a ball-shaped region B on a spatial slice of Minkowski space, showing the evolution generated by B H . A conformal transformation maps D to a hyperbolic cylinder time H d  1

  total entropy variation can be written as



  If the quantum field state is varied away from the vacuum, with an excitation length scale much longer than the diamond size,



  is the change in the energy density in comparison to the vacuum state and X

  the d + 2 dimensional Newton constant. Intuitively, this suggests that the minimal surface A

L

  the euclidean lagrangian. The normalization factor of the partition function ensures that 1   Tr

1

 1

1 , n 

 1n needed for the calculation of the entanglement entropy of a single interval ] sheets sequentially joined to each other on the segment x ∈

  The partition function (here L[ϕ](x, τ) is the local lagrangian density)

  ) ), the integral on the right hand side is evaluated as similar to Zamolodchikov's c-theorem[11a,b]. We thus recover (s)

4  and Az B 4 

 44 from [31]. The other components of the magnetic displacement current Ar B are not vanishing but they are much suppressed 20 consistently with Fig.2 from [31].

.

  Applying D operator to the Bianchi identity and using the Jacobi identity and the equations of motion, we get

.

  Hence the dual London equation (17) is obtained.Most estimates in the literature refer to the gluon mass, related to the

21

 21

  Hubble constant is defined as, see eq.(3.20,3.21,3.22) from[START_REF] Grasso | Potential s in the Early Universe[END_REF].

  by use of the Compton length as:

  charge e , mass m , Compton wave-length mc C  and so-called "critical" electric field

 2  2 

 22 For spherically symmetric pulses, the shear and vorticity vanish, and the Raychaudhuri equation, Eq. (36) from [36]be the initial area of the black hole in the distant past, where 0 M is its initial mass, then we have In this approximation, the change in the mass of the black hole is the result obtained by calculating the change in mass directly from Eq. (23) as Here, it was defined an "effective magnetic field", effB , in terms of the total energy density in the magnetic field of MF Vortex, Since the quarks generated inside nucleons or in EW bubbles are generated by a pulsating process , or, we have obtained the classical formula for deformation. The build of spacetime is obtained by using well-known Inflation models [34a,b], which in our opinion is nothing else than a spreading of entanglement-energy source-horizon end, where the scale leaving the horizon at a given epoch is directly related to the number ) (Nof e -folds of slow-roll inflation that occur after the epoch of horizon exit. Indeed, since H -the Hubble length is slowly varying, we have scale leaving the horizon at the end slow-roll inflation, or usually ]

  that the energy density is the sum of the energy densities of the n individual copies.

	Hence the expression of  Z does indeed define local fields at	( 1 u	) 0 ,	and	( 1 v	) 0 ,	in the multi-
	copy model [23]. Notice that n  ~ can be identified with	n  (and in fact they were called 

n  and n 

  . In other words the pulse is transferred from nucleons via electromagnetic field as glued Riemann sheets to CFT viewed as a hologram, that it means the greater contribution to expansion.

	To note, that the gravitational potential for Earth is	U		Earth 2 GM R Earth		6 . 3 	10	32	J	; the stress-
	energy tensor is:	T	j	 		U	44 . 1	10 	8 		n	nucleons		2 . 4	10 	12 	J	;
	n		M	10	27 		6		10	51
	nucleons		Earth
	1 or the expansion due of EW epoch since continue till ) (   vol V V R ; where ] , ] [ 10  1  10 1 [  14 v   10  s 10 8 . 3 . 6   4 . 4 3 m A     6   0 . 1 3 C    A A 10 10    So, the deformation is 10 2 57    V V R vol ] [ 10 5 . 1 15 s    ; v today since 8 . 6   , that corresponds with well known Einstein ring, A here ] [ 10 5 . 6 6 1 m R H A      .

v e 


Finally, a representative end-to-end experiment was performed to evaluate the benefit of such technologies.

Model driven Engineering

To deal with the increasing complexity of space systems while maintaining flight software high validation level, software engineering techniques must evolve accordingly. Model-based engineering aims at making complexity management easier by constructing virtual representations that enable early prediction of behaviour and performance of a system, as well as documentation and code generation.

Among the various modelling techniques, UML is the one that fits best the onboard software domain. The additional modelling effort required during the specification and design phases is recovered during validation phases through automatic code and test generation. Maintenance effort and in particular regression testing are significantly reduced.

Test generator prototype implementation

During Acceleo generator is an EPL open source "model to code" generator which is user configurable threw templates. OCL and Activity generators make used of a java Platform Specific Model developed by Astrium. The Generated java code is target independent, the target code interface, relative to observability and commandability is hand coded in the bench interface instance specified in <BENCH_IF> stereotype. Today's ECSS standard is focussed on documents and it is quite difficult to produce and easy to read documentation from models. Using direct access to models offers the possibility to navigate and follow the links between model entities but modelling tools do not support and formalized model review process to ensure completeness of the review. Using modelling also puts strong requirements on the people involved in the review: mastering UML and OCL language requires some specific training compared to natural language documents.

Conclusion

The

1. 1 Figure 1 :

 11 Figure 1: Model-drive engineering in the V-cycle

Figure 2 :

 2 Figure 2: Impact of automatic test generation on the software development cycle

Stereotypes

  Stereotypes are used to clarify the model with label information added in the graphical description and tag useful information on UML elements (class, attributes, and operations) for code generation. Two profiles have been defined for the study:• Testing profile allow tagging model classes to identify design and test models and to specify test bench interface. • Tmtc profile allow tagging model class properties and operations to specify observability and commandability attributes.

Figure 4 :

 4 Figure 4: Testing profile stereotypes

Figure 6 :

 6 Figure 6: Test experiment configuration

UML for Validation: Experimenting automatic test generation for flight software validation

	A. Philippe HYOUNET 1 , B. Jérémie POULY 2
	1: ASTRIUM SAS, 31 rue des cosmonautes 31402 Toulouse Cedex 4
	philippe.hyounet@astrium.eads.net
	Phone : +33 (0)5 62 19 5125
	Fax : +33 (0)5 62 19 71 58
	2: CNES, 18 avenue Edouard Belin 31401 Toulouse Cedex 9
	jeremie.pouly@cnes.fr
	Phone : +33 (0)5 61 28 23 67
	Fax : +33 (0)5 61 27 45 5

Abstract:

UML for validation is a CNES study that aims at prototyping and experimenting automatic test generation technologies in the context of a modelbased approach applied to on-board software development and tests. Starting from real test cases and test procedures taken from state-of-the-art onboard software, we first applied a reverse engineering methodology to obtain an augmented software specification model, i.e. ready to support automated test generation. In parallel, we defined and prototyped a test generation tool using innovative model-based technologies based on EMF (Eclipse Modeling Framework).

  the UML for validation study, we have implemented a model-based process at architectural design phase level. Whenever it was possible we used innovative open source model-based technologies, such as model transformation and code generation. Thus we managed to reduce time and cost for the development of the test generator prototype, while ensuring reuse capability.

	2.1 Actors and relationships
	Implementing model-based engineering
	methodology involves different actors due to the
	numerous skills required. Relationships between
	actors has been identified and illustrated on the
	figure below for integration test phase relative to
	architectural design validation. Similar process
	should be applicable for validation tests phase.
	Analysis model Analysis model Analysis model Analysis model Analysis model Analysis model			Functional Functional Functional
	SPECIFICATION SPECIFICATION SPECIFICATION SPECIFICATION SPECIFICATION SPECIFICATION					Test Test Test	VALIDATION VALIDATION VALIDATION VALIDATION VALIDATION VALIDATION
						TESTS TESTS TESTS TESTS TESTS TESTS
	ARCHITECTURAL DESIGN ARCHITECTURAL DESIGN ARCHITECTURAL DESIGN ARCHITECTURAL DESIGN ARCHITECTURAL DESIGN ARCHITECTURAL DESIGN	Design model Design model Design model	Integration Test Integration Test Integration Test	INTEGRATION TESTS INTEGRATION TESTS INTEGRATION TESTS INTEGRATION TESTS INTEGRATION INTEGRATION TESTS TESTS
		DETAILLED DESIGN DETAILLED DESIGN DETAILLED DESIGN DETAILLED DESIGN DETAILLED DESIGN DETAILLED DESIGN	Implementation model Implementation model Implementation model	Component Test Component Test Component Test	COMPONENT TEST COMPONENT TEST COMPONENT TEST COMPONENT TEST COMPONENT TEST COMPONENT TEST
				CODING CODING CODING CODING CODING CODING
	Software development team Software development team	Software validation team Software validation team
	Design model Design model Design model			inheritance inheritance	Test model Test model Test model	Expand model Expand model
						For test definition For test definition
				Test Code Generator Test Code Generator Test Code Generator	Integration Tests Integration Integration Integration Tests Tests Tests
						Bench Bench Bench Bench
						IF IF IF IF
	Generator development team Generator development team		Test bench team Test bench team
	Figure 3: Actors involved in UML validation process
	UML validation process involves the following actors:
	• The software development team which
	provides UML design models to test
	(corresponding to Architectural Design
	document) to validation team.
	• The software validation team which
	implements UML test models corresponding
	to test specification document and specifies
	test	code	generator	to	generator
	development team. Then the validation team
	gets the environment to automatically
	generate test procedures and performs them
	on the test bench. • The generator development team which
	implements the test code generator tool
	according validation team specifications.

• The test bench team which implements test bench interface specific code. Note: specifications documents, such as Architectural Design and test Specification, are part of the UML model and will be automatically generated by the UML modeller tool. For the study use case, this part is out of scope and specifications document are used for model implementation. 2.2 Modelling A model-based engineering approach has been applied. The software architecture design model, which substitutes to software specification, has been implemented in UML. Selected test objectives have been added to the UML model using Object Constraint Language. Observability and commandability, involved in OCL constraints, has been specified by adding stereotypes in the UML model. Finally, test procedures have been added using UML activity diagrams.

OCL GEN OCL GEN UML Model UML Model OBSW UML models OCL constraints Opaque exp <pre> <comment> Comments used to add test information </comment> <ocl> (OCL expressions) </ocl> </pre> <post> <comment> Comments used to add test information </comment> <ocl> (OCL ex pr es si ons ) </ocl> </post> OCL constraints Opaque exp <pre> <comment> Comments used to add test information </comment> <ocl> (OCL expressions) </ocl> </pre> <post> <comment> Comments used to add test information </comment> <ocl> (OCL ex pr es si ons ) </ocl> </post> OCL constraints Opaque exp <pre> <comment> Comments used to add test information </comment> <ocl> (OCL expressions) </ocl> </pre> <post> <comment> Comments used to add test information </comment> <ocl> (OCL ex pr es si ons ) </ocl> </post> + ACCELEO ACCELEO Class

  Test procedures were automatically generated from the model. Stubbed bench interface have been produced to integrate OCL model implementation under eclipse native java execution platform.

				3.1 Simops test environment
				Simops test environment is connected to a numerical
				simulation of the equipments and the on-board
				computer. The connection is made of TM/TC
	UML model UML model		Java code Java code	interface and processor emulator services such as read/write of memory symbols. It allows executing
				the real On-Board Software in a representative
	PowerCtrl PowerCtrl	ACCELEO GEN ACCELEO GEN	PowerCtrl.java PowerCtrl.java	configuration.
				Java test procedures, automatically generated under
			PowerCtrlVal.java PowerCtrlVal.java	Topcased tool, have been executed on Simops test
		AC CE LE O GE N AC CE LE O GE N		control environment.
	PowerCtrlVal PowerCtrlVal	OCL GEN OCL GEN	PowerCtrlValOcl.java PowerCtrlValOcl.java
		SE QU EN CE GE N SE QU EN CE GE N
			PowerCtrlTestSequence.java PowerCtrlTestSequence.java
	Figure 11: Test java code architecture
				Native Tests Execution Native Tests Execution
			Test Development Test Development
		PC Linux 2.6 PC Linux 2.6
				JavaSimops 4.5 JavaSimops 4.5	OBSW OBSW OBSW
		Test Execution Test Execution
				Simops Tests Execution Simops Tests Execution

  UML for validation study demonstrated the feasibility of using automatic test generation to produce test scripts that can be executed in a real onboard software environment. It also allowed benchmarking a new methodology for future validation process, which combines software development and validation teams. A consequent effort should be performed by actors to define and implement the test behaviour model, but the quality relative to the coherence in the test engineery process is improved as all information's are defined in the model. During maintenance phase, the evaluation impact of software modification and corresponding test regression is also improved. The test generator prototype implementation highlight that if OCL is adapted to specify unitary test, its syntax is complex and real type is limited as it not support both floating and double types. Model based methodology is innovative for space applications, which get very specific quality constraints. Applying such process required a robust and high quality model design tool. Topcased demonstrated enough robustness to perform test modelisation on dimensioning models, but an industrial development is mandatory to fulfil space quality standards.

Code

Class Code

Unit

Use case experiment

The experimentation is built on a subset of Pleiades on-board software. It is based on two major equipments:

• Modelling and test code generation have been performed using Topcased software environment toolkit.


Claire Guégan

Franck Corbier

Claire Guegan

How to reduce qualification time for new safety automated systems on rail infrastructure

Keywords: Signalling, Transportation, Model based Design, Progressive Integration, Validation, Safety, Quality, Qualification, EN-50128

With 10 million passengers transported every day, RATP has been investing in transport modernisation to cope with the continuous growth of traffic, to offer an up-to-date response to passenger expectations, and to optimize economical and environmental performances. Figure 1 : The metro of Paris, more than 110 years of history As part of the Paris Metro modernisation program, RATP chose to develop a novel metro management system called OURAGAN.

Leveraging communication based train control, OURAGAN allows traffic operators to reduce the headway between two trains in complete safety, as more trains are available for passengers during peak hours. Such systems become increasingly complex as well as difficult to integrate and qualify. This paper will present specific tools and methods used to dramatically reduce time and costs devoted to on-site tests.

Introduction

The major difficulty resides in the connection and integration of safety systems (electronic control units distributed on network) with original and existing safety signalling systems, that gives different response times and input data. Traditional tests are usually performed at night when the traffic is closed. To be completed, on-site tests require a lot of time (around 1000 nights) and resources (test engineers but also drivers and traffic operators).

RATP

introduced exchangeability into the OURAGAN project, turning it into Generic OURAGAN project. This strategy offers flexibility, guarantees system supply from multiple sources and provides cost efficiency. It became essential then to focus on methods and tools based on new "virtualisation" concepts which apply to specification, validation and training. In order to qualify the OURAGAN system, RATP launched the "System Integration & Qualification Bench" (BIQS) project. This project implements specific methods and tools that scale to the complexity level of systems such as OURAGAN, making system integration and qualification phases significantly more effective.

OURAGAN Hardware Architecture

Major issues are to interface the OURAGAN system with existing instrumentation (historical knowledge) of the line (campaign, signalling), the local control station and the central exploitation control of the line.

Integration and Qualification needs

Main objectives of the BIQS bench are:  to improve integration phases, set up and validation of a new line using tests management on the laboratory bench,  to monitor the OURAGAN system during its life cycle (operation and maintenance activities) and to support investigations and assist diagnosis,  to test and validate future evolutions and changes of the system,  to serve as a reference for exchangeability.

Objectives and tasks of the system qualification bench are based on the following concepts:  Ability to simulate an entire line with real time constraints and representative behaviour,  Ability to integrate and co-simulate different models (train, line, traffic, signalling, safety rules, autopilot…),  Ability to swap a target model with the real target without heavy reconfiguration,  Ability to emulate the data transmission system,  Ability to obtains degraded modes of system functions by fault insertion,  Ability to place the test cases in automatic mode as well as in interactive mode,  Capacity for flexibility and extension of the configuration line,  Ability to provide HMIs to facilitate the analysis,  Ability to re-play incidents recorded on the line.

All these concepts put together represent a major innovation in the context of RATP projects.

Because OURAGAN markets are allotted, the manufacturers which support implementation of "bundles" have a fragmented view of the overall system and the interfaces shall only be liable for their services. Final integration of system components remains a matter of on-site testing, on the basis of tests of actual situation on the line. Moreover, realization of such an integration and qualification bench requires pooling knowledge from different actors, who are either dedicated to control systems, either experts of simulation, either managers able to cope with complex organization and systems.

To limit the risks of developing such a system, RATP has decided to start with a first step called "demonstrator", intended to confirm feasibility of main concepts involved. This demonstration is based on the implementation of recognized industrial knowhow, in the field of system simulation and qualification benches development.

Consequently, the main requirements for this bench have been classified into three categories:  Support for integration and validation  Support for systems maintenance  Qualification of a new supplier, in compliance with OURAGAN exchangeability requirement 3.1. Support for integration and validation Objective is to validate the system off-line, to reduce on-site qualification time and avoid operation disruptions.

Support for systems maintenance

One primary purpose is to maintain the system in operation and to detect root causes of anomalies occurring in exploitation, using registered data (black box). The idea is to strip incidents, to analyze registered events and to visualize/check them with friendly HMIs and tools. Such services can automatically create scenarios (tests vectors) to replay real-time situations on the bench.

Qualification of a new supplier, in compliance with OURAGAN exchangeability requirements

The BIQS bench helps qualify the target provided by a new manufacturer, before adding it in to the reference list of compliant OURAGAN equipments. This target will undergo standard test sets and both final and expected results should match for compliance: standard test procedures are applied to new targets and test results are automatically compared with the expected results.

BIQS Hardware Architecture

To meet the needs of integration and validation, the BIQS bench qualification system needs to simulate the complete OURAGAN system environment, to host the electronic control units of the entire system and allow test cases to be run. This complete environment, including signalling, line, and trains, as well as all OURAGAN safety and control functions have been modelled and simulated using ControlBuild. Automatic test scripts (traffic and failure modes) have been applied on the line model, providing fast and comprehensive analysis results.

A uniqueness of the BIQS bench lies in the fact that the real ECUs developed to meet the OURAGAN system can be, at will, either connected to or simulated on the bench. In addition, a device created by Vendor A may be replaced by another ECU made by Supplier B, alternatively by a simulation model. The goal of this first implementation is to create a virtual model of the line, which, from the electronic equipments perspective, will behave exactly like the real one. Signalling model: The current Paris Metro signalling system that ensures safety control is primarily done in electrical hardware. This system will have to coexist with the new electronic controlled system. It is therefore necessary, for the qualification bench, to develop the model of the signalling hardware. The rolling stock model is simplified in order to deliver the necessary interfaces to drive the train model "by a conductor". The panel driving cab has been generalized to enable the same driving modes whatever rolling stock types can be.

Autopilot models

Real electronic processing units (automatic pilots) can either be present or absent on the test bench. Hence, it has been necessary to develop models (virtual clones) that are able to simulate the functions supported by the non present target. These models can be dynamically enabled or disabled depending on the presence of the real equipment.

Test scripts

The qualification bench can be operated manually or in automated modes. In manual mode, the GUI for the simulation models (line, signalling, cabs, rolling stock ...) enable testers to drive the trains along the line (route development), to verify the correct operation of the real (and simulated) equipment and create failures to validate the safety functions and faulty modes. ControlBuild allows test engineers to describe test scripts that act on the models, so as to trigger actions related to nominal operation modes (eg locate a train, wake up the train, change the driving modes, accelerate or brake) or to cause abnormal situations (e.g., forcing a failure on a part of the system or on an equipment). Test cases are sequences of operations providing events on inputs and measurements on outputs. These procedures can also be automatically executed on the qualification test bench. The main test script loads the initial context of the current test (fixed state of simulated equipments and environment) and then sequentially executes all code instructions according to the desired test. At the same time, other scenarios may simulate failures, trigger events (expected or not) and force the state of some equipment models. Test scripts provide code instructions for the configuration of inputs/outputs and communications interfaces between the test bench and the real hardware ECUs to qualify. These instructions allow test engineers to cause faults on all interfaces and communications.

Physical interfaces of the bench

The objective of the test bench is to qualify hardware targets before their integration on the site (or inside the train). For this purpose, it is necessary to connect the targets to the bench; the BIQS test bench provides inputs/outputs and communication subsystems.

Inputs/outputs subsystem

The acquisition subsystem is expected to stimulate the inputs of physical targets, to measure the outputs value of the equipments, additionally to supply real targets with power. For each signal, the subsystem ensures adaptation of electrical channels, digitization of analog sensor levels and time stamping of events. The BIQS test bench hardware subsystem is also able to support standard or specific communication networks. A configuration editor allows customization of inputs/outputs cards and communication protocols on the qualification bench. The simulation of malfunctions of the communication system allows test and safety engineers to verify the capability of real equipments, detect faulty behaviours, and take the right decision (continue, stop, secures, alert…).

Conclusion

This System Integration and Qualification Bench project demonstrates the key advantages of using proven simulation technologies to address safety automation issues. Key factors of success reside in the versatility of the simulation tool used, i.e. ControlBuild, particularly well suited for transportation sectors and in the flexibility of the methods and process used (from Model to HIL). Gains achieved by implementing this solution measure up to the costs of downtime and operation of the real infrastructure when system qualification tests are performed on site.

"One day of tests with simulation represents up to ten nights of onsite tests!"

Beyond this novel "test bench" adoption, RATP will address other activities pertaining to the system engineering process.

This Model Based Testing technology seems to be promising, in terms of technical purposes, for validation of specifications before system development. The high-level languages provided by ControlBuild allows the designer to easily describe the different environment models of the line (campaign, signalling, power distribution), to reuse rolling stock models and to prototype new automation requirements (safety control or not). These use cases can be validated by the different project stakeholders (engineering, safety department, traffic operation engineers…). Since the model is representative of the system, the integration and qualification bench may be a support for investigations once the system is in use. All events detected in real operation can be inserted in the test bench for analysis. The model could also be used to train the RATP workers on how to manage the traffic though the station when the communication with the automatic or central control room is off. It would then be possible to create situations, events and incidents that should never happen in the real life: the objective is to increase officer's awareness of incidents that may occur and to give them the ability to take the right decisions in stressful situations.

Figure 2 :

 2 Figure 2: OURAGAN in its environment

Figure 3 :

 3 Figure 3: System Integration and Qualification Bench

Figure 4 :

 4 Figure 4: Map of the test line "Porte de Charenton"

Figure 5 :

 5 Figure 5: Physical line with traffic

Figure 6 :

 6 Figure 6: Signalling schemes

Figure 7 :

 7 Figure 7: Visualization panel in station

Figure 9 :

 9 Figure 9: Panel driving cab

Figure 10 :

 10 Figure 10: Display of the autopilot interfaces states

Figure 11 :

 11 Figure 11: Test scripts editor and generated test reports

Figure 12

 12 Figure 12: I/O and networks configuration

Figure 13 :

 13 Figure 13: Spy, Data login and Communication monitoring

  in the rolling stock PAS AutoPilot along the line PCC Poste de Commande Centralisé PMI Poste de Manoeuvre Informatisé RATP Régie Autonome de Transport Parisien SQV Surveillance Quai Voie STD Data Transmission System