General non-rotating perfect-fluid solution with an abelian spacelike C_3 including only one isometry

TL;DR

This paper presents a new general solution for non-rotating perfect-fluid spacetimes with specific symmetries, extending previous solutions and including important cosmological models like FLRW, with potential applications in perturbation theory.

Contribution

It introduces a novel family of solutions characterized by an abelian C_3 symmetry acting on spacelike hypersurfaces, extending prior work with new properties and special limiting cases.

Findings

Contains FLRW particular cases.

Includes solutions with non-abelian G_2 symmetry.

Features limiting cases with non-orthogonal group actions.

Abstract

The general solution for non-rotating perfect-fluid spacetimes admitting one Killing vector and two conformal (non-isometric) Killing vectors spanning an abelian three-dimensional conformal algebra (C_3) acting on spacelike hypersurfaces is presented. It is of Petrov type D; some properties of the family such as matter contents are given. This family turns out to be an extension of a solution recently given in \cite{SeS} using completely different methods. The family contains Friedman-Lema\^{\i}tre-Robertson-Walker particular cases and could be useful as a test for the different FLRW perturbation schemes. There are two very interesting limiting cases, one with a non-abelian G_2 and another with an abelian G_2 acting non-orthogonally transitively on spacelike surfaces and with the fluid velocity non-orthogonal to the group orbits. No examples are known to the authors in these classes.