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

Jan E. Aman, Narit Pidokrajt

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 values of $2n - d + 3$ is 0, 1 or 2. For black holes with $2n < d - 3$ the Ruppeiner curvature diverges but they have no extremal limits. 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 takes place. We conjecture that the membrane phase ultraspinning MP black holes is reached at the minimum temperature in the case $2n < d - 3$ which is where the Ruppeiner curvature diverges.