Conformal Symmetries of Locally Rotationally Symmetric Spacetimes

TL;DR

This paper explores conformal symmetries in Locally Rotationally Symmetric spacetimes, revealing inherent homothetic symmetries and their implications, especially in rotating, twisting, and perfect fluid cases.

Contribution

It identifies the existence of a natural homothetic symmetry in general LRS spacetimes with rotation and twist, and analyzes its geometric and physical consequences.

Findings

Homothetic symmetry exists in rotating, twisting LRS spacetimes.

Null Killing horizons form when heat flux reaches extremal values.

Restrictions on conformal geometry for perfect fluid cases.

Abstract

In this paper we investigate conformal symmetries in Locally Rotationally Symmetric (LRS) spacetimes using a semitetrad covariant formalism. We demonstrate that a general LRS spacetime which rotates and spatially twists simultaneously has an inherent homothetic symmetry in the plane spanned by the fluid flow lines and the preferred spatial direction. We discuss the nature and consequence of this homothetic symmetry showing that a null Killing horizon arises when the heat flux has an extremal value. We also consider the special case of a perfect fluid and the restriction on the conformal geometry.