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Central singularity of three-dimensional Kerr–de Sitter black holes

Mauro Carlone1 and Wolfgang Mück1,2,*

  • *Contact author: mueck@na.infn.it
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Phys. Rev. D 113, 044001 – Published 2 February, 2026

DOI: https://doi.org/10.1103/dt1y-96pg

Abstract

For three-dimensional Kerr–de Sitter space-time, we find the singular energy-momentum and spin tensor sources that generate the nontrivial 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.

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Phys. Rev. D 113, 044001– Published 2 February, 2026
  • Received 6 November 2025
  • Accepted 13 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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