Extreme Kerr throat geometry: A vacuum analog ofAdS2×S2

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 $\mathrm{SL}\mathrm{}(2,R)\mathrm{}\times \mathrm{U}\mathrm{}\left(1\right).$ We show that many of the properties of this solution are similar to the ${\mathrm{AdS}}_2{\times \mathrm{S}}^2$ 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.