Dynamical Black Holes in 2+1 Dimensions

TL;DR

This paper explores the structure and evolution of a non-stationary black hole solution in 2+1 dimensional gravity theories, analyzing horizons, singularities, and entropy proposals.

Contribution

It presents the first detailed analysis of a non-stationary black hole in 2+1 dimensions, including horizon dynamics and entropy calculations using the Kodama vector.

Findings

Existence of a timelike singularity without angular momentum

Outer horizon can grow or shrink over time

Kodama vector correctly computes entropy for stationary black holes

Abstract

We investigate the global structure of a recently discovered simple exact, non-stationary solution of topologically massive and new massive gravity with the asymptotic charges of an undeformed BTZ black hole. We establish the existence of a timelike singularity in the causal structure of the spacetime even in the absence of angular momentum. The dynamical trapping and event horizons are determined and we investigate the evolution of the outer horizon showing that it may increase or decrease with time, depending on the value of the mass parameter. Finally, we test two proposals for dynamical entropy on this solution, one of them depending on the Kodama vector. In addition we show that the Kodama vector leads to the correct entropy for all stationary black holes in 2+1 dimensions.