Conformal symmetries of spherical spacetimes

TL;DR

This paper explores the conformal symmetries of spherically symmetric spacetimes, deriving general conditions and identifying specific solutions, including those with fluid flow and dynamic properties, expanding previous static results.

Contribution

It provides a comprehensive derivation of conformal Killing vectors in spherical spacetimes without matter restrictions, extending static spacetime results to dynamic, fluid-filled scenarios.

Findings

Derived general conformal Killing symmetry conditions.

Identified inheriting conformal symmetry vectors.

Found a specific solution with expanding, accelerating, shearing fluid.

Abstract

We investigate the conformal geometry of spherically symmetric spacetimes in general without specifying the form of the matter distribution. The general conformal Killing symmetry is obtained subject to a number of integrability conditions. Previous results relating to static spacetimes are shown to be a special case of our solution. The general inheriting conformal symmetry vector, which maps fluid flow lines conformally onto fluid flow lines, is generated and the integrability conditions are shown to be satisfied. We show that there exists a hypersurface orthogonal conformal Killing vector in an exact solution of Einstein's equations for a relativistic fluid which is expanding, accelerating and shearing.