THERMODYNAMICS OF A BLACK-HOLE IN A CAVITY

We present a unified thermodynamic description of configurations consisting of self-gravitating radiation with or without a black hole. We compute the thermal fluctuations and evaluate where they will induce a transition from metastable configurations towards stable ones. We show that the probability of finding such a transition is exponentially small. This indicates that, in a sequence of quasi-equilibrium configurations, the system will remain in metastable states until it approaches very closely the critical point beyond which no metastable configuration exists. Near that point, we relate the divergence of local temperature fluctuations to the approach of instability of the whole system, thereby generalizing the usual fluctuation analysis to cases where long-range forces are present. When angular momentum is added to the cavity, the above picture is slightly modified. Nevertheless, at high angular momentum, the black hole loses most of its mass before it reaches the critical point at which it evaporates completely.