Notes on Black Hole Phase Transitions

In these notes we present a summary of existing ideas about phase transitions of black hole spacetimes in semiclassical gravity and offer some thoughts on three possible scenarios by which these transitions could take place. Our first theme is ilustrated by a quantum atomic black hole system, generalizing to finite-temperature a model originally offered by Bekenstein. In this equilibrium atomic model, the black hole phase transition is realized as the abrupt excitation of a high energy state, suggesting analogies with the study of two-level atoms. Our second theme argues that the black hole system shares similarities with the defect-mediated Kosterlitz-Thouless transition in condensed matter. These similarities suggest that the black hole phase transition may be more fully understood by focusing upon the dynamics of black holes and white holes, the spacetime analogy of vortex and anti-vortex topological defects. Finally we compare the black hole phase transition to another transition driven by an exponentially increasing density of states, the Hagedorn transition first found in hadron physics in the context of dual models or the old string theory. In modern string theory, the Hagedorn transition is linked by the Maldacena conjecture to the Hawking-Page black hole phase transition in Anti-deSitter space, as observed by Witten. Understanding the dynamics of the Hagedorn transition may thus yield insight into the dynamics of the black hole phase transition. We argue that characteristics of the Hagedorn transition are already contained within classical string systems where a nonperturbative and dynamical analysis is possible.