The near-horizon limit of the extreme rotating d = 5 black hole as a homogeneous spacetime

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 [−1, 1], is locally isomorphic to a homogeneous non-symmetric spacetime corresponding to an element of the one-parameter family of coset spaces SO(2, 1) × 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).