Hypersurface homogeneous locally rotationally symmetric spacetimes admitting conformal symmetries

TL;DR

This paper classifies hypersurface homogeneous locally rotationally symmetric spacetimes with conformal symmetries, explicitly determining their symmetry vectors and analyzing their algebraic structures, including applications to static and perfect fluid spacetimes.

Contribution

It systematically classifies LRS spacetimes with conformal symmetries, developing new methods for certain classes and applying results to static and perfect fluid cases.

Findings

Classification of conformal algebra for all static LRS spacetimes

Explicit determination of symmetry vectors for hypersurface homogeneous LRS spacetimes

Identification of perfect fluid LRS spacetimes admitting proper conformal symmetries

Abstract

All hypersurface homogeneous locally rotationally symmetric spacetimes which admit conformal symmetries are determined and the symmetry vectors are given explicitly. It is shown that these spacetimes must be considered in two sets. One set containing Ellis Class II and the other containing Ellis Class I, III LRS spacetimes. The determination of the conformal algebra in the first set is achieved by systematizing and completing results on the determination of CKVs in 2+2 decomposable spacetimes. In the second set new methods are developed. The results are applied to obtain the classification of the conformal algebra of all static LRS spacetimes in terms of geometrical variables. Furthermore all perfect fluid nontilted LRS spacetimes which admit proper conformal symmetries are determined and the physical properties some of them are discussed.