Exact solutions in 3D gravity with torsion

TL;DR

This paper explores exact charged and uncharged black hole solutions in 3D gravity with torsion, revealing connections to Chern-Simons black holes, TMG at the chiral point, and Godel solutions, while recovering BTZ black holes in specific limits.

Contribution

It provides new exact solutions in 3D gravity with torsion, linking them to known models like Chern-Simons black holes and TMG, and extends the understanding of black holes in Riemann-Cartan spacetime.

Findings

Charged black hole solutions in 3D gravity with torsion are derived.

Solutions reduce to known Chern-Simons black holes when torsion vanishes.

Logarithmic solutions of TMG are also solutions of the MB model at a fixed point.

Abstract

We study the three-dimensional gravity with torsion given by the Mielke-Baekler (MB) model coupled to gravitational Chern-Simons term, and that possess electric charge described by Maxwell-Chern-Simons electrodynamics. We find and discuss this theory's charged black holes solutions and uncharged solutions. We find that for vanishing torsion our solutions by means of a coordinate transformation can be written as three-dimensional Chern-Simons black holes. We also discuss a special case of this theory, Topologically Massive Gravity (TMG) at chiral point, and we show that the logarithmic solution of TMG is also a solution of the MB model at a fixed point in the space of parameters. Furthermore, we show that our solutions generalize Godel type solutions in a particular case. Also, we recover BTZ black hole in Riemann-Cartan spacetime for vanishing charge.