A complete set of integrals and solutions to the Szekeres system

Gierzkiewicz, Anna; Golda, Zdzislaw A.

doi:10.1016/j.physleta.2018.05.038

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…From (52) it follows that the equation [72], X [1] (L) + L t, q i ,q i ξ =ḟ (53) which is called Noether symmetry condition, or Noether's first theorem.…”

Section: Noether's Theoremsmentioning

confidence: 99%

“…There is not unique method to construct conservation laws of dynamical systems. Some of the different approaches which have been applied in cosmological studies are, (a) point symmetries (b) dynamical symmetries [41,42], (c) Cartan symmetries [43], (d) nonlocal symmetries [44][45][46][47] (e) singularity analysis [48], (f) Hojman approach [49,50], (g) Darboux polynomial [51,52], (h) automorphism [53][54][55], (i) Galois group [56].…”

Section: Symmetries and Integrabilitymentioning

confidence: 99%

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Conservation laws and exact solutions in Brans–Dicke cosmology with a scalar field

Paliathanasis

2019

Gen Relativ Gravit

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Scalar-tensor theories have drawn the attention of cosmologist for the past few years because they can provide mechanism to explain the observable phenomena. Moreover, the results of scalar-tensor theories can be applied in higher-order theories of gravity. In this work, we consider a Brans-Dicke scalar field cosmological model that includes a second scalar field minimally coupled to gravity. For the second scalar field we consider the two cases that there exist and there is not any interaction with the Brans-Dicke scalar field. For the two models of our consideration we prove the existence of scaling and de Sitter solutions. Furthermore, we perform an Obsiannikov's classification for the field equations, where we find all the point and contact transformations which leave the gravitational Action Integral invariant. Conservation laws are determined and we show how these can be applied to infer about the integrability of the cosmological models and find new analytic solutions. 95.35.+d, 95.36.+x

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“…From (52) it follows that the equation [72], X [1] (L) + L t, q i ,q i ξ =ḟ (53) which is called Noether symmetry condition, or Noether's first theorem.…”

Section: Noether's Theoremsmentioning

confidence: 99%

Section: Symmetries and Integrabilitymentioning

confidence: 99%

Conservation laws and exact solutions in Brans–Dicke cosmology with a scalar field

Paliathanasis

2019

Gen Relativ Gravit

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“…Specifically, three time-independent conservation laws where derived which were used to reduce the four-dimensional Szekeres system into a two-dimensional system. Moreover, the analytic solution for the reduced two-dimensional system is presented in [19]. Furthermore, in [20] a Lagrangian function was derived for the Szekeres system, which means that the system (1)-( 2) follows from a variational principle.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics and evolution for the Szekeres system with nonzero cosmological constant term

Paliathanasis¹,

León²

2021

Preprint

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The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for Einstein field equations in R 4 . In this study, we investigate the behavior of trajectories in the presence of cosmological constant. It has been shown that the Szekeres system is a Hamiltonian dynamical system. It admits at least two conservation laws, h and I 0 which indicate the integrability of the Hamiltonian system. We solve the Hamilton-Jacobi equation, and we reduce the Szekeres system from R 4 to an equivalent system defined in R 2 . Global dynamics are studied where we find that there exists an attractor in the finite regime only for positive valued cosmological constant and I 0 < 2.08. Otherwise, trajectories reach infinity. For I 0 > 0 the origin of trajectories in R 2 is also at infinity. Finally, we investigate the evolution of physical properties by using dimensionless variables different from that of Hubble-normalization conducing to a dynamical system in R 5 . We see that the attractor at the finite regime in R 5 is related with the de Sitter universe for a positive cosmological constant.

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Cyclic Szekeres universes

Barrow

Paliathanasis

2019

Eur. Phys. J. C

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We consider the Szekeres universe with an inhomogeneous dust fluid and a homogeneous and isotropic ghost matter source with equation of state pg = (γ − 1) ρg, where γ is a constant. The field equations determine two families of spacetimes which describe homogeneous Kantowski-Sachs universes and inhomogeneous Friedmann universe. The ghost field Einstein permits static and cyclic solutions to exist. The stability of the Einstein static and cyclic solutions are studied with a critical point analysis.

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A complete set of integrals and solutions to the Szekeres system

Cited by 4 publications

References 15 publications

Conservation laws and exact solutions in Brans–Dicke cosmology with a scalar field

Conservation laws and exact solutions in Brans–Dicke cosmology with a scalar field

Global dynamics and evolution for the Szekeres system with nonzero cosmological constant term

Cyclic Szekeres universes

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