perfect-fluid cosmologies with a proper conformal Killing vector

DOI10.1088/0264-9381/14/8/026zbMATH Open0886.53072arXivgr-qc/0202060OpenAlexW3102658667MaRDI QIDQ4354815

Author name not available (Why is that?)

Publication date: 17 September 1997

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Abstract: We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The three-dimensional conformal group is restricted to the case when the two-dimensional abelian isometry subalgebra is an ideal and it is also assumed to act on non-null hypersurfaces (both, spacelike and timelike cases are studied). We consider both, diagonal and non-diagonal metrics and find all the perfect-fluid solutions under these assumptions (except those already known). We find four families of solutions, each one containing arbitrary parameters for which no differential equations remain to be integrated. We write the line-elements in a simplified form and perform a detailed study for each of these solutions, giving the kinematical quantities of the fluid velocity vector, the energy-density and pressure, values of the parameters for which the energy conditions are fulfilled everywhere, the Petrov type, the singularities in the spacetimes and the Friedmann-Lemaitre-Robertson-Walker metrics contained in each family.

Full work available at URL: https://arxiv.org/abs/gr-qc/0202060

zbMATH Keywords

cosmology Einstein field equations Petrov type of spacetimes

Mathematics Subject Classification ID

Relativistic cosmology (83F05) Applications of differential geometry to physics (53Z05) Exact solutions to problems in general relativity and gravitational theory (83C15)