Lower-dimensional Gauss-Bonnet Gravity and BTZ Black Holes

Understand

We consider the $D\to 3$ limit of Gauss-Bonnet gravity.

• We find two distinct but similar versions of the theory and obtain black hole solutions for each.
• For one theory the solution is an interesting generalization of the BTZ black hole that does not have constant curvature but whose thermodynamics is identical.
• The other theory admits a solution that is asymptotically AdS but does not approach the BTZ black hole in the limit of small Gauss-Bonnet coupling.