Curvature singularity of the distributional BTZ black hole geometry

TL;DR

This paper investigates the distributional curvature of the non-rotating BTZ black hole, revealing a delta-function singularity at the origin linked to a point source, and discusses invariance properties.

Contribution

It provides a detailed analysis of the distributional curvature tensor for the BTZ black hole, highlighting the singularity structure and invariance aspects.

Findings

Curvature tensor has delta-function singularity at the origin.

Singularity corresponds to a point source via Einstein equations.

Results are coordinate-invariant and independent of differentiable structure.

Abstract

For the non-rotating BTZ black hole, the distributional curvature tensor field is found. It is shown to have singular parts proportional to a $\delta$-distribution with support at the origin. This singularity is related, through Einstein field equations, to a point source. Coordinate invariance and independence on the choice of differentiable structure of the results are addressed.