New class of LRS spacetimes with simultaneous rotation and spatial twist

TL;DR

This paper introduces a new class of Locally Rotationally Symmetric spacetimes that exhibit both rotation and spatial twist simultaneously, with potential applications in modeling rotating astrophysical stars.

Contribution

It establishes the existence, necessary conditions, and properties of these novel solutions, including their self-similarity and relation to heat flux.

Findings

Solutions require non-zero, bounded heat flux.

Solutions are self-similar.

Applicable as first approximations for rotating stars.

Abstract

We establish the existence and find the necessary and sufficient conditions for a new class of solutions of Locally Rotationally Symmetric spacetimes that have non vanishing rotation and spatial twist simultaneously. We transparently show that the existence of such solutions demand non vanishing and bounded heat flux and these solutions are self similar. We provide a brief algorithm indicating how to solve the system of field equations with the given Cauchy data on an initial spacelike Cauchy surface. Finally we argue that these solutions can be used as a first approximation from spherical symmetry to study rotating, inhomogeneous, dynamic and radiating astrophysical stars.