Black hole information geometry and critical phenomena

Applications of information geometry to black hole physics are discussed. We focus mainly on the outcomes of this research program. The type of information geometry we utilize in this approach is the Ruppeiner geometry defined on the state space of a given thermodynamic system in equilibrium. The Ruppeiner geometry can be used to analyze stability and critical phenomena in black hole physics with results consistent with those obtained by the Poincare stability analysis for black holes and black rings. Furthermore other physical phenomena are well encoded in the Ruppeiner metric such as the sign of specific heat and the extremality of the solutions. The information geometric approach has opened up new perspectives on the statistical mechanics of black holes - an unsettled subject necessary for the emerging theory of quantum gravity. We discuss in detail the use of information geometry for addressing ultraspinning phases of the (higher-dimensional) Myers-Perry (MP) black holes. We conjecture that the membrane phase of ultraspinning MP black holes is reached at the minimum temperature in the case of $2n < d - 3$ (with $n$ the number of angular momenta and $d$ the number of dimensions), which corresponds to the singularity of the Ruppeiner metric.