Thermodynamics for higher dimensional rotating black holes with variable Newton constant *

The extensivity for the thermodynamics of general D -dimensional rotating black holes with or without a cosmological constant can be proved analytically, provided that the effective number of microscopic degrees of freedom and the chemical potential are given respectively as , where G is the variable Newton constant, is the Euclidean action, and L is a constant length scale. In the cases without a cosmological constant, i.e., the Myers-Perry black holes, the physical mass and the intensive variables can be expressed as explicit macro state functions in the extensive variables in a simple and compact form, which allows for an analytical calculation of the heat capacity. The results indicate that the Myers-Perry black holes with zero, one, and k equal rotation parameters are all thermodynamically unstable.