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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>O</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:mo>,</a:mo> <a:mn>3</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> 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.