On the extremality and ultraspinning instability of Myers-Perry black holes

Abstract

We use a contact geometric method to study Myers-Perry (MP) black holes in arbitrary dimensions with arbitrary angular momenta. We have shown that the MP black holes of dimension d with n equal nonzero spins and 2n ≥ d − 3 all have extremal limits as expected and that we should classify MP black holes in three series depending on whether the value of 2n − d + 3 is 0, 1 or 2. For black holes with 2n < d − 3 the Ruppeiner curvature diverges although they have no extremal limits. In order to have an ultraspinning mode at least one spin of the MP black hole must be set to zero. Our result agrees with others in the literature where the authors are able to establish the minimum temperature surface on which the membrane phase of ultraspinning MP black holes occurs. We conjecture that the membrane phase of ultraspinning MP black holes is reached around the minimum temperature in the case 2n < d − 3 which is where the Ruppeiner curvature diverges.