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

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.