A remark on black holes of Chern-Simons gravities in $2n+1$ dimensions: $n=1,2,3$

TL;DR

The paper demonstrates that Chern-Simons gravities in odd dimensions admit black hole solutions similar to the BTZ black hole, and these solutions are unique for dimensions n=1,2,3.

Contribution

It explicitly constructs and verifies the uniqueness of BTZ-like black hole solutions in Chern-Simons gravities for dimensions n=1,2,3.

Findings

Solutions described by the same lapse function as BTZ black hole

Explicit solutions for n=1,2,3

Solutions are unique in these dimensions

Abstract

It is shown that Chern-Simons gravities in $2n+1$ dimensions admit solutions described by the same lapse function which describes the BTZ black hole in the $n=1$ case. This has been carried out explicitly for $n=1,2,3$. Moreover, it is seen that these solutions are unique.