Axially Symmetric, Spatially Homothetic Spacetimes

TL;DR

This paper explores how spatial homothety relates to metric separability in axially symmetric spacetimes, showing that such solutions allow arbitrary density profiles and do not produce locally naked singularities during collapse.

Contribution

It establishes a link between spatial homothety and metric separability in axially symmetric spacetimes, expanding understanding of gravitational collapse outcomes.

Findings

Density profiles are arbitrary in these spacetimes.

Solutions do not lead to locally naked singularities.

The approach relates homothety to metric function separability.

Abstract

We show that the existence of appropriate spatial homothetic Killing vectors is directly related to the separability of the metric functions for axially symmetric spacetimes. The density profile for such spacetimes is (spatially) arbitrary and admits any equation of state for the matter in the spacetime. When used for studying axisymmetric gravitational collapse, such solutions do not result in a locally naked singularity.