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Cosmological Constant and Local Gravity
We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the linearized set of equations for the metric perturbations, in the Lo...
Autores principales: | , , |
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Formato: | info:eu-repo/semantics/article |
Lenguaje: | eng |
Publicado: |
Phys. Rev. D
2009
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.1103/PhysRevD.81.084002 http://cds.cern.ch/record/1213885 |
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author | Bernabeu, Jose Espinoza, Catalina Mavromatos, Nick E |
author_facet | Bernabeu, Jose Espinoza, Catalina Mavromatos, Nick E |
author_sort | Bernabeu, Jose |
collection | CERN |
description | We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the linearized set of equations for the metric perturbations, in the Lorentz gauge, which are not spherically symmetric, but they rather exhibit a cylindrical symmetry. We find that the components of the gravitational field satisfying the appropriate Poisson equations have the property of ensuring that a scalar potential can be constructed, in which both contributions, from ordinary matter and $\Lambda > 0$, are attractive. In addition, there is a novel tensor potential, induced by the pressure density, in which the effect of the cosmological constant is repulsive. We also linearize the Schwarzschild-de Sitter exact solution of Einstein's equations (due to a generalization of Birkhoff's theorem) in the domain between the two horizons. We manage to transform it first to a gauge in which the 3-space metric is conformally flat and, then, make an additional coordinate transformation leading to the Lorentz gauge conditions. We compare our non-spherically symmetric solution with the linearized Schwarzschild-de Sitter metric, when the latter is transformed to the Lorentz gauge, and we find agreement. The resulting metric, however, does not acquire a proper Newtonian form in terms of the unique scalar potential that solves the corresponding Poisson equation. Nevertheless, our solution is stable, in the sense that the physical energy density is positive. |
format | info:eu-repo/semantics/article |
id | cern-1213885 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2009 |
publisher | Phys. Rev. D |
record_format | invenio |
spelling | cern-12138852019-09-30T06:29:59Z doi:10.1103/PhysRevD.81.084002 http://cds.cern.ch/record/1213885 eng Bernabeu, Jose Espinoza, Catalina Mavromatos, Nick E Cosmological Constant and Local Gravity General Relativity and Cosmology We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the linearized set of equations for the metric perturbations, in the Lorentz gauge, which are not spherically symmetric, but they rather exhibit a cylindrical symmetry. We find that the components of the gravitational field satisfying the appropriate Poisson equations have the property of ensuring that a scalar potential can be constructed, in which both contributions, from ordinary matter and $\Lambda > 0$, are attractive. In addition, there is a novel tensor potential, induced by the pressure density, in which the effect of the cosmological constant is repulsive. We also linearize the Schwarzschild-de Sitter exact solution of Einstein's equations (due to a generalization of Birkhoff's theorem) in the domain between the two horizons. We manage to transform it first to a gauge in which the 3-space metric is conformally flat and, then, make an additional coordinate transformation leading to the Lorentz gauge conditions. We compare our non-spherically symmetric solution with the linearized Schwarzschild-de Sitter metric, when the latter is transformed to the Lorentz gauge, and we find agreement. The resulting metric, however, does not acquire a proper Newtonian form in terms of the unique scalar potential that solves the corresponding Poisson equation. Nevertheless, our solution is stable, in the sense that the physical energy density is positive. info:eu-repo/grantAgreement/EC/FP7/237920 info:eu-repo/semantics/openAccess Education Level info:eu-repo/semantics/article http://cds.cern.ch/record/1213885 Phys. Rev. D Phys. Rev. D, (2010) pp. 084002 2009-10-20 |
spellingShingle | General Relativity and Cosmology Bernabeu, Jose Espinoza, Catalina Mavromatos, Nick E Cosmological Constant and Local Gravity |
title | Cosmological Constant and Local Gravity |
title_full | Cosmological Constant and Local Gravity |
title_fullStr | Cosmological Constant and Local Gravity |
title_full_unstemmed | Cosmological Constant and Local Gravity |
title_short | Cosmological Constant and Local Gravity |
title_sort | cosmological constant and local gravity |
topic | General Relativity and Cosmology |
url | https://dx.doi.org/10.1103/PhysRevD.81.084002 http://cds.cern.ch/record/1213885 http://cds.cern.ch/record/1213885 |
work_keys_str_mv | AT bernabeujose cosmologicalconstantandlocalgravity AT espinozacatalina cosmologicalconstantandlocalgravity AT mavromatosnicke cosmologicalconstantandlocalgravity |