  We review and extend previous results regarding the stability and
thermodynamics of Anti-de Sitter (AdS) spacetime at finite temperature. Using a
combination of analytic and numerical techniques, we compute the energy,
temperature, and entropy of perfect fluid stars in asymptotically AdS
spacetimes. We find that at sufficiently high temperature (in the canonical
ensemble) or energy (in the microcanonical ensemble) these configurations
develop dynamical instabilities, which presumably lead to the formation of a
black hole. We extend our analysis to the case of $AdS \times S$
compactifications stabilized by flux (such as those that arise in supergravity
and string theory), and find that the inclusion of the sphere does not
substantially alter these results. We then map out the phase structure of these
theories in the canonical and microcanonical ensembles, paying attention to
inequivalence of these ensembles for global anti-de Sitter space. With a
certain scaling limit, the critical temperature can be parametrically lower
than the string temperature, so that supergravity is a good description at the
instability point. We comment on the implications of this for the unitarity of
black holes.
