On explicit thermodynamic functions and extremal limits of Myers–Perry black holes
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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.
KeywordsBlack Hole Black Hole Solution Black Ring Kerr Black Hole Extremal Limit
Narit Pidokrajt acknowledges the KoF group, Fysikum, Stockholms Universitet for the warm hospitality, in particular to Hans Hansson for lending him a nice computer screen. NP would also like to thank the Royal Swedish Academy of Sciences (KVA) for supporting this project through the grant FOA10V-116. We kindly thank Ingemar Bengtsson for his enlightening and many useful comments, and acknowledge Gary Gibbons for giving us some useful information. NP would like to thank Roberto Emparan for stimulating discussions on MP black holes with equal spins while he was a visitor in Barcelona.
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