Exact Description of Black Holes on Branes II: Comparison with BTZ Black Holes and Black Strings

TL;DR

This paper analyzes black hole solutions on branes with a negative cosmological constant, showing their relation to BTZ black holes and black strings, and providing exact solutions for rotating cases.

Contribution

It extends previous work to include a negative cosmological constant, deriving exact solutions for rotating black holes and analyzing the transition between black strings and localized black holes.

Findings

Large mass solutions are BTZ black holes and black strings.

Localized black holes have exponential corrections to BTZ.

Transition point between black string and black hole configurations.

Abstract

We extend our recent discussion of four-dimensional black holes bound to a two-brane to include a negative cosmological constant on the brane. We find that for large masses, the solutions are precisely BTZ black holes on the brane, and BTZ `black strings' in the bulk. For smaller masses, there are localized black holes which look like BTZ with corrections that fall off exponentially. We compute when the maximum entropy configuration changes from the black string to the black hole. We also present exact solutions describing rotating black holes on two-branes which are either asymptotically flat or asymptotically $AdS_3$. The mass and angular momentum on the brane agree with that in the bulk.