$Λ^{mu}_ν$ geometries from the point of view of different observers

Details $Λ^{mu}_ν$ geometries from the point of view of different observers $Λ^{mu}_ν$ geometries from the point of view of different observers

2003-10-06

arxiv.org/abs/gr-qc/0310031v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, 11 figures, Talk at the Fourth International Conference on Physics Beyond the Standard Model "Beyond the Desert'03",

Scientific paper

$\Lambda^{\mu}_{\nu}$-geometry is a geometry with a variable cosmological term described by a second-rank symmetric tensor $\Lambda^{\mu}_{\nu}$ whose asymptotics are Einstein cosmological term $\Lambda \delta ^{\mu}_{\nu}$ at the origin and $\lambda \delta ^{\mu}_{\nu}$ at infinity (with $\lambda < \Lambda$). It corresponds to extension of the algebraic structure of the Einstein cosmological term $\Lambda \delta ^{\mu}_{\nu}$ in such a way that a scalar $\Lambda$ describing vacuum energy density as $\rho_{vac}=8\pi G \Lambda$ (with $\rho_{vac}$=const by virtue of the Bianchi identities), becomes explicite related to the appropriate component, $\Lambda^0_0$, of an appropriate stress-energy tensor, $T^{\mu}_{\nu}=8\pi G\Lambda^{\mu}_{\nu}$ whose vacuum properties follow from its symmetry, $T_0^0=T_1^1$, and whose variability follows from the contracted Bianchi identities. In the spherically symmetric case existence of such geometries in frame of GR follows from imposing on Einstein equations requirements of finiteness of the ADM mass $m$, and of regularity of density and pressures. Dependently on parameters $m$ and $q=\sqrt{\Lambda /\lambda}$, $\Lambda^{\mu}_{\nu}$ geometry describes five types of configurations. We summarize here the results which tell us how these configurations look from the point of view of different observers: a static observer, a Lemaitre co-moving observer, and a Kantowski-Sachs observer.

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