The Near-Horizon Limit of the Extreme Rotating d=5 Black Hole as a Homogenous Spacetime

TL;DR

This paper demonstrates that the near-horizon geometry of an extremal rotating five-dimensional black hole is a homogeneous, non-symmetric spacetime described by a specific coset space, revealing its geometric structure.

Contribution

It identifies the local isomorphism of the near-horizon limit to a particular homogeneous coset space, extending understanding of black hole geometries in supergravity.

Findings

Near-horizon geometry is a homogeneous non-symmetric spacetime.

The spacetime corresponds to a coset space SO(2,1) x SO(3)/SO(2)_j.

The structure holds for any rotation parameter j in [-1,1].

Abstract

We show that the spacetime of the near-horizon limit of the extreme rotating d=5 black hole, which is maximally supersymmetric in N=2,d=5 supergravity for any value of the rotation parameter j in [-1,1], is locally isomorphic to a homogeneous non-symmetric spacetime corresponding to an element of the 1-parameter family of coset spaces SO(2,1)x SO(3)/SO(2)_j in which the subgroup SO(2)_j is a combination of the two SO(2) subgroups of SO(2,1) and SO(3).