Einstein's equations constrained by homogeneous and isotropic expansion: Initial value problems and applications

In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are naturally interpreted as spatially homogeneous and isotropic...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: Gomes, Leandro G, Nogueira, Marcelo A C, Lucas Ruiz dos Santos
Format: Article
Language:English
Subjects:
Astronomical models
Boundary value problems
Constraints
Cosmology
Einstein equations
Energy transfer
Exact solutions
Relativity
Uniqueness theorems
Online Access:Get full text
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Summary:In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are naturally interpreted as spatially homogeneous and isotropic on ``large scales". In order to show the well-posedness and applicability of such a scheme, we specialize in a class of spacetimes filled with the general homogeneous perfect fluid and inhomogeneous viscoelastic matter. We prove the existence, uniqueness, and relative stability of solutions, and an additional inequality for the energy density. As a consequence of our theorems, a new mechanism of energy transfer appears involving the different components of matter. A class of exact solutions is also obtained to exemplify the general results.
ISSN:2331-8422