Regular Article - Theoretical Physics
On explicit thermodynamic functions and extremal limits of Myers–Perry black holes
Department of Physics, Stockholm University, 106 91, Stockholm, Sweden
Revised: 4 July 2013
Published online: 7 November 2013
We study thermodynamic geometries of Myers–Perry (MP) black holes with arbitrary number of angular momenta. This geometric method allows us to visualize thermodynamic state spaces of the MP black holes as wedges embedded in a Minkowski-like parameter space. The opening angles of these wedges are uniquely determined by the number of spacetime dimensions d, and the number of angular momenta associated with the MP black holes, n. The geometric structure captures extremal limits of the MP black holes, and hence serves as a method for identifying the black hole’s extremal limit. We propose that classification of the MP black hole solutions should based on these uncovered structures. In order for the ultraspinning regime to exist, at least one of the angular momenta has to be set to zero. Finally, we conjecture that the membrane phase of ultraspinning MP black holes is reached at the minimum temperature in the case where 2n<d−3 based on the thermodynamic curvature obtained.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013