Phase transition, critical behavior, and critical exponents of Myers-Perry black holes

The critical behavior of Myers-Perry black holes with equal angular momenta in even dimensions are studied. We include the corrections beyond the semiclassical approximation on Hawking temperature in the grand canonical ensemble. Having done so, we find that the critical behavior and critical exponents of Myers-Perry black holes correspond to those of a Van der Waals liquid-gas where this analogy holds in any dimension. Also, using Ehrenfest's equations, we calculate the order of the phase transition in the semiclassical approximation for the canonical ensemble and beyond the semiclassical approximation for the grand canonical ensemble near the critical point. Finally, the Ruppeiner curvature formula is used to investigate the thermodynamic geometry of Myers-Perry black holes.