The Extreme Kerr Throat Geometry: A Vacuum Analog of AdS_2 x S^2

TL;DR

This paper analyzes the near horizon geometry of extreme rotating black holes, revealing a nonsingular vacuum solution with enhanced symmetry, similar to AdS_2 x S^2, and discusses potential dual quantum descriptions and higher-dimensional generalizations.

Contribution

It introduces a new vacuum solution for the near horizon limit of extreme rotating black holes with enhanced symmetry, analogous to AdS_2 x S^2, and explores its properties and higher-dimensional extensions.

Findings

The limiting metric is a nonsingular vacuum solution with SL(2,R) x U(1) symmetry.

The boundary at infinity is timelike, similar to AdS_2 x S^2.

Potential for a dual quantum mechanical description is suggested.

Abstract

We study the near horizon limit of a four dimensional extreme rotating black hole. The limiting metric is a completely nonsingular vacuum solution, with an enhanced symmetry group SL(2,R) x U(1). We show that many of the properties of this solution are similar to the AdS_2 x S^2 geometry arising in the near horizon limit of extreme charged black holes. In particular, the boundary at infinity is a timelike surface. This suggests the possibility of a dual quantum mechanical description. A five dimensional generalization is also discussed.