G_2 Perfect-Fluid Cosmologies with a proper conformal Killing vector

TL;DR

This paper classifies perfect-fluid cosmological solutions with specific symmetries, identifying four families of solutions with detailed physical and geometric properties, including energy conditions and singularities.

Contribution

It provides a comprehensive classification of G_2 perfect-fluid cosmologies with conformal symmetries, extending known solutions and analyzing their physical and geometric features.

Findings

Identified four families of solutions with arbitrary parameters.

Derived conditions for energy conditions to hold.

Analyzed singularities and Petrov types of solutions.

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.