Accelerating black hole in 2+1 dimensions and 3+1 black (st)ring

TL;DR

This paper introduces a new solution in 2+1 dimensions describing an accelerating black hole, explores its embedding in 3+1 dimensions, and discusses related structures like black strings and black rings.

Contribution

It presents a novel C-metric type solution for 2+1D gravity with cosmological constant and explores its embeddings as black strings and black rings in 3+1D.

Findings

New 2+1D accelerating black hole solution

Embedding of the solution as a black string and black ring

Admissibility of positive cosmological constant

Abstract

A C-metric type solution for general relativity with cosmological constant is presented in 2+1 dimensions. It is interpreted as a three-dimensional black hole accelerated by a strut. Positive values of the cosmological constant are admissible too. Some embeddings of this metric in the 3+1 space-time are considered: accelerating BTZ black string and a black ring where the gravitational force is sustained by the acceleration.