Λ ^μ _υ Geometries from the Point of View of Different Observers

Abstract

Λ ^μ _υ -geometry is a geometry with a variable cosmological term described by a second-rank symmetric tensor Λ ^μ _υ whose asymptotics are Einstein cosmological term Λδ ^μ _υ at the origin and λδ ^μ _υ at infinity (with λ < Λ). It corresponds to extension of the algebraic structure of the Einstein cosmological term Λδ ^μ _υ in such a way that a scalar Λ describing vacuum energy density as (with p _uac = 8πGΛ (with p _uac =const by virtue of the Bianchi identities), becomes explicite related to the appropriate component, Λ ⁰₀ , of an appropriate stress-energy tensor, T ^μ _υ whose vacuum properties follow from its symmetry, T ⁰₀ = T ¹₁ , 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 regularity of density and finiteness of the ADM mass, and dominant energy condition on 521-13 either weak energy condition and regularity of pressures. Dependently on parameters m and $q = \sqrt {\Lambda /\lambda } ,\Lambda _\nu ^\mu$ geometry describes five types of configurations. We summarize here the results which tell us how these configurations look front the point of view of different observers: a static observer, a Lemaitre co-moving observer, and a Kantowski-Sachs observer.