Questions of stability near black hole critical points

In this paper, we discuss how thermal fluctuations can effect the stability of charged black holes when close to certain critical points. Our novel treatment utilizes the black hole area spectrum (taken to be evenly spaced) and makes an important distinction between fixed and fluctuating charge systems. The discussion begins with a summary of a recent technical paper. We then go on to consider the issue of stability when the system approaches the critical points of interest. These include the Hawking-Page phase transition, a transition that is relevant to Reissner-Nordstr\"om black holes and various extremal-limiting cases.