Exotic black hole solution in teleparallel theory of (2+1)-dimensional gravity

TL;DR

This paper explores a unique black hole solution in a (2+1)-dimensional teleparallel gravity theory, which also satisfies Einstein's vacuum equations, revealing novel properties of vacuum regions in three-dimensional spacetime.

Contribution

It presents a new black hole solution in teleparallel gravity that also solves Einstein's equations, highlighting the non-triviality of vacuum regions in 3D spacetime.

Findings

Solution describes a black hole in a flat-land in Einstein theory.

Coordinate transformations are singular at the horizon and origin.

Vacuum regions in 3D Einstein theory can be locally non-trivial.

Abstract

A black hole solution in a teleparallel theory of (2+1)-dimensional gravity, given in a previous paper, is examined. This solution is also a solution of the three-dimensional vacuum Einstein equation with a vanishing cosmological constant. Remarkable is the fact that this solution gives a black hole in a \lq \lq flat-land" in the Einstein theory and a Newtonian limit. Coordinate transformations to \lq \lq Minkowskian" coordinates, however, are singular not only at the origin, but also on the event horizon. {\em In the three-dimensional Einstein theory, vacuum regions of space-times can be locally non-trivial}.