Exact inhomogeneous cosmologies whose source is a radiation-matter mixture with consistent thermodynamics

Sussman, Roberto A.; Pavón, Diego

doi:10.1103/physrevd.60.104023

Cited by 20 publications

(51 citation statements)

References 36 publications

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“…This case is interesting as it corresponds to the generalisation of the classic LTB model [31,39] as well as to the Sussman and Pavon [18,40] example we will use later. The major difference from the general case is the absence of Hessian trace, 1 α D a D a α, and traceless Hessian, ǫ, in the equations (III.47), (III.48) and (III.49).…”

Section: Dynamical System Restricted To Geodesic Flowmentioning

confidence: 99%

“…To illustrate our results we turn our attention to an exact solution derived by Sussman and Pavón for a spherically symmetric model with a matter content consisting of a combination of dust and radiation that exhibits anisotropic stress, but no heat fluxes and Λ = 0 [18].…”

Section: A Sussman-pavón Exact Solution: Radiation and Mattermentioning

confidence: 99%

“…In order to do that we need to translate the metric (II.1) in the LTB form used in [18], following their assumption of comoving, i.e. geodesic, flow (here the velocity of light c is reintroduced) n a SP = cδ a t .…”

Section: A Sussman-pavón Exact Solution: Radiation and Mattermentioning

confidence: 99%

“…To illustrate our results we analyse a particular solution with dust and radiation. Such a solution stems from the work of Sussman and Pavón [18] where, albeit the generality of their initial formalism, they analysed only the thermodynamic aspects of the spatially flat spherical solution. We find the conditions caracterising the matter and radiation content to fulfill the existence of a separating shell.…”

Section: Introductionmentioning

confidence: 99%

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Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures

2013

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We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We resort to a 3 + 1 splitting and obtain gauge invariant conditions relating intrinsic spacetimes quantities to properties of the matter source. We find that the dividing shell is defined by a generalization of the Tolman-Oppenheimer-Volkoff equilibrium condition. The latter establishes a balance between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharp mass inside the separating shell and by the pressure fluxes. This defines a local equilibrium condition, but conveys also a non-local character given the definition of the Misner-Sharp mass. By the same token, it is also a generalized thermodynamical equation of state as usually interpreted for the perfect fluid case, which now has the novel feature of involving both the isotropic and the anisotropic stress. We have cast the governing equations in terms of local, gauge invariant quantities which are revealing of the role played by the anisotropic pressures and inhomogeneous electric part of the Weyl tensor. We analyse a particular solution with dust and radiation that provides an illustration of our conditions. In addition, our gauge invariant formalism not only encompasses the cracking process from Herrera and coworkers but also reveals transparently the interplay and importance of the shear and of the anisotropic stresses.

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Section: Dynamical System Restricted To Geodesic Flowmentioning

confidence: 99%

Section: A Sussman-pavón Exact Solution: Radiation and Mattermentioning

confidence: 99%

Section: A Sussman-pavón Exact Solution: Radiation and Mattermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures

2013

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We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We resort to a 3 + 1 splitting and obtain gauge invariant conditions relating intrinsic spacetimes quantities to properties of the matter source. We find that the dividing shell is defined by a generalization of the Tolman-Oppenheimer-Volkoff equilibrium condition. The latter establishes a balance between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharp mass inside the separating shell and by the pressure fluxes. This defines a local equilibrium condition, but conveys also a non-local character given the definition of the Misner-Sharp mass. By the same token, it is also a generalized thermodynamical equation of state as usually interpreted for the perfect fluid case, which now has the novel feature of involving both the isotropic and the anisotropic stress. We have cast the governing equations in terms of local, gauge invariant quantities which are revealing of the role played by the anisotropic pressures and inhomogeneous electric part of the Weyl tensor. We analyse a particular solution with dust and radiation that provides an illustration of our conditions. In addition, our gauge invariant formalism not only encompasses the cracking process from Herrera and coworkers but also reveals transparently the interplay and importance of the shear and of the anisotropic stresses.

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“…Given Eqn. (8) it is interesting to relate the condition (4) to the Hamiltonian constraint that generalizes the Friedman equation…”

mentioning

confidence: 99%

Spherically symmetric models: Separating expansion from contraction in models with anisotropic pressures

Mimoso¹,

Delliou²,

Mena³

2012

AIP Conference Proceedings

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We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We find that the dividing shell is defined by a relation between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharpe mass inside the separating shell and by the pressure fluxes. This balance is a generalization of the Tolman-OppenheimerVolkoff equilibrium condition which defines a local equilibrium condition, but conveys also a nonlocal character given the definition of the Misner-Sharpe mass. We present a particular solution with dust and radiation that provides an illustration of our results.The universe close to us exhibits structures below certain scales that seem to be immune to the overall expansion of the universe. This reflects two different gravitational behaviors, and usually the dynamics corresponding to the structures that have undergone non-linear collapse is treated under the approximation that Newton's gravitational theory is valid without residual acceleration. However, this approach does not tell us with exactitude what is the critical scale where the latter approximation starts to be valid, nor does it explain in a non-perturbative way how the collapse of over-dense patches decouples from the large-scale expansion. For this purpose one requires a fully general relativistic approach where an exact solution exhibiting the two competing behaviors and allowing us to characterize how the separation between them comes about. It is the understanding of this interplay between collapsing and expanding regions within the theory of general relativity (GR) that we aim to address here.In previous works we have investigated the present issue in models with spherical symmetry and with a perfect fluid [1, 2] . Here we briefly report our findings when we overcome the limitations of a perfect fluid description of the non-equilibrium setting under focus. We thus consider here an anisotropic fluid.We resort to a 3 + 1 splitting, and assess the existence and stability of a dividing shell separating expanding and collapsing regions, in a gauge invariant way.

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Constraining the spectrum of cosmological perturbations from statistical thermal fluctuations

Graef

2021

Physics Letters B

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Exact inhomogeneous cosmologies whose source is a radiation-matter mixture with consistent thermodynamics

Cited by 20 publications

References 36 publications

Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures

Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures

Spherically symmetric models: Separating expansion from contraction in models with anisotropic pressures

Constraining the spectrum of cosmological perturbations from statistical thermal fluctuations

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