Central Singularity of Three-Dimensional Kerr-de Sitter Black Holes

TL;DR

This paper identifies the singular energy-momentum and spin sources in three-dimensional Kerr-de Sitter spacetime, providing insights into the geometry and potential observable algebra for local observers.

Contribution

It introduces a method to determine the singular sources generating the non-trivial geometry using holonomy analysis of the Chern-Simons gauge field.

Findings

Derived the symmetric, conserved energy-momentum tensor for the singularity.

Determined the mass and angular velocity of the spinning point particle.

Linked the holonomy to the singular source terms at the center.

Abstract

For three-dimensional Kerr-de Sitter space-time, we find the singular energy-momentum and spin tensor sources that generate the non-trivial geometry. The energy-momentum tensor is symmetric, conserved and compatible with a spinning massive point particle whose mass and angular velocity we determine. The calculation is based on the analysis of the holonomy for a closed loop around the singularity of the $SO(1,3)$ Chern-Simons gauge field appropriate for gravity in the presence of a positive cosmological constant. This holonomy is related, via the non-abelian Stokes theorem, to the singular source terms at the center. Our results may be helpful for a better understanding of the algebra of observables of a local observer in the Kerr-de Sitter space-time.