Dynamical black holes in 2+1 dimensions

We investigate the global structure of a recently discovered simple exact, nonstationary solution of topologically massive and new massive gravity with the asymptotic charges of an undeformed Banados-Teitelboim-Zanelli 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.