Thermodynamic stability of Kerr black holes

Critical behavior for the dilaton black holes

“…The Davies' points are just such turning points. The divergent behavior of some second moments at the Davies' points means only that the stability for Kerr-Newman black holes is changed [16]. However this has nothing to do with the second-order phase transitions.…”

“…Wilczek and his collaborators [15] argued that the thermodynamic description is inadequate for some extremal black holes and their behavior resembles the normal elementary particles, strings, or extended objects. In addition, Kaburaki and his collaborators [16] found that the Davies' points in fact are turning points, which are related to the changes of stability. Also they claimed that the divergence of heat capacity at those points does not mean the occurrance of phase transition.…”

A Zeroth Law Compatible Model to Kerr Black Hole Thermodynamics

“…Although the new formal logarithmic entropy function (27) of Kerr black holes is additive for composition, the Hessian method for stability analysis cannot be used, because (like in the Schwarzschild problem) the heat capacities are divergent. Nevertheless, the Poincaré method can still provide information about the stability of the system.…”

“…The standard stability analysis of extensive systems however is not generally applicable to black holes, since it strongly depends on the additivity of the entropy function [26], which is clearly not true for the Bekenstein-Hawking entropy of black holes. To avoid the inapplicability of the classical Hessian analysis to nonadditive systems, Kaburaki et al [27] proposed the Poincaré turning point method [28] to investigate the thermodynamic stability of black holes. This method is a topological approach that does not depend on the additivity of the entropy function, and it has been widely applied to problems in astrophysical and gravitating systems [26,27,[29][30][31] where-as we have already mentioned-entropy functions with nonextensive nature tend to appear frequently due to the long-range interaction property of the gravitational field.…”

“…C J is negative for h < h c and positive for h > h c . Kaburaki et al [27] considered the thermodynamic stability of standard Kerr black holes by using the Poincaré turning point method. They concluded that isolated Kerr black holes are thermodynamically stable with respect to axisymmetric perturbations.…”