Cosmological constant and local gravity

Journal Article · Thu Apr 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.084002· OSTI ID:21413431

Bernabeu, Jose; Espinoza, Catalina; Mavromatos, Nick E ^[1]

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1. Departamento de Fisica Teorica and IFIC, Universidad de Valencia-CSIC, E-46100, Burjassot, Valencia (Spain) and CERN, Theory Division, CH-1211 Geneva 23 (Switzerland)

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.

• OSTI ID: 21413431
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 8; Other Information: DOI: 10.1103/PhysRevD.81.084002; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
COMPARATIVE EVALUATIONS
COSMOLOGICAL CONSTANT
CYLINDRICAL CONFIGURATION
DE SITTER SPACE
DENSITY
DISTURBANCES
EINSTEIN FIELD EQUATIONS
ENERGY DENSITY
EXACT SOLUTIONS
GAUGE INVARIANCE
GRAVITATIONAL FIELDS
LORENTZ INVARIANCE
METRICS
MINKOWSKI SPACE
PERTURBATION THEORY
POISSON EQUATION
SCHWARZSCHILD METRIC
SPACE-TIME
SYMMETRY
TRANSFORMATIONS
CONFIGURATION
DIFFERENTIAL EQUATIONS
EQUATIONS
EVALUATION
FIELD EQUATIONS
INVARIANCE PRINCIPLES
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
SPACE