2+1 Black Hole with a Dynamical Conical Singularity

TL;DR

This paper presents novel 2+1 dimensional black hole solutions with a dynamical conical singularity at the horizon, challenging the traditional entropy-area relation and exploring their implications in quantum gravity path integrals.

Contribution

It introduces new black hole solutions with dynamical conical singularities in 2+1 gravity and analyzes their impact on black hole entropy and quantum gravity path integrals.

Findings

Entropy proportional to total opening angle, not area

Solutions depend on particle path windings around the horizon

Potential implications for quantum gravity path integral summation

Abstract

We find black hole solutions to Euclidean 2+1 gravity coupled to a relativistic particle which have a dynamical conical singularity at the horizon. These solutions mimic the tree level contribution to the partition function of gravity coupled to a quantum field theory. They are found to violate the standard area law for black hole entropy, their entropy being proportional to the total opening angle. Since each solution depends on the number of windings of the particle path around the horizon, the significance of their summation in the path integral is considered.