Counting the Microstates of a Kerr Black Hole

TL;DR

This paper demonstrates how the microstates of an extremal Kerr black hole can be exactly counted by relating it to known microstates of a D0-D6 black hole in string theory, revealing insights into black hole entropy and topology.

Contribution

It introduces a method to count Kerr black hole microstates by lifting to M-theory and relating to D0-D6 black holes, providing an exact entropy match.

Findings

Exact microstate count for extremal Kerr black hole

Relation between Kerr and D0-D6 black holes in M-theory

Topology of the event horizon is ill-defined in M-theory

Abstract

We show that an extremal Kerr black hole, appropriately lifted to M-theory, can be transformed to a Kaluza-Klein black hole in M-theory, or a D0-D6 charged black hole in string theory. Since all the microstates of the latter have recently been identified, one can exactly reproduce the entropy of an extremal Kerr black hole. We also show that the topology of the event horizon is not well defined in M-theory.