Black Holes in Three Dimensional Topological Gravity

TL;DR

This paper explores black hole solutions in (2+1)-dimensional topological gravity without a cosmological constant, revealing unique properties of energy, angular momentum, and entropy influenced by topological matter fields.

Contribution

It introduces novel black hole solutions in topological gravity and analyzes how topological matter alters conserved quantities and entropy compared to Einstein gravity.

Findings

Energy and angular momentum are reversed in interpretation compared to general relativity.

Entropy depends on the inner horizon circumference, not the outer horizon.

Two new possible black hole solutions are proposed.

Abstract

We investigate the black hole solution to (2+1)-dimensional gravity coupled to topological matter, with a vanishing cosmological constant. We calculate the total energy, angular momentum and entropy of the black hole in this model and compare with results obtained in Einstein gravity. We find that the theory with topological matter reverses the identification of energy and angular momentum with the parameters in the metric, compared with general relativity, and that the entropy is determined by the circumference of the inner rather than the outer horizon. We speculate that this results from the contribution of the topological matter fields to the conserved currents. We also briefly discuss two new possible (2+1)-dimensional black holes.