We compute the properties of a class of charged black holes in anti-de Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der Waals-Maxwell liquid-gas system. In that case, the phases are controlled by the universal ''cusp'' and ''swallowtail'' shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes. ͓S0556-2821͑99͒02316-4͔

Gravitational collapse of matter trapped on a brane will produce a black hole on the brane. We discuss such black holes in the models of Randall and Sundrum where our universe is viewed as a domain wall in five-dimensional anti-de Sitter space. We present evidence that a non-rotating uncharged black hole on the domain wall is described by a ''black cigar'' solution in five dimensions.

The physical properties of Reissner-Nordström black holes in (nϩ1)-dimensional anti-de Sitter spacetime are related, by a holographic map, to the physics of a class of n-dimensional field theories coupled to a background global current. Motivated by that fact, and the recent observations of the striking similarity between the thermodynamic phase structure of these black holes ͑in the canonical ensemble͒ and that of the van der Waals-Maxwell liquid-gas system, we explore the physics in more detail. We study fluctuations and stability within the equilibrium thermodynamics, examining the specific heats and electrical permittivity of the holes, and consider the analogue of the Clayperon equation at the phase boundaries. Consequently, we refine the phase diagrams in the canonical and grand canonical ensembles. We study the interesting physics in the neighborhood of the critical point in the canonical ensemble. There is a second order phase transition found there, and that region is characterized by a Landau-Ginzburg model with A 3 potential. The holographically dual field theories provide the description of the microscopic degrees of freedom which underlie all of the thermodynamics, as can be seen by examining the form of the microscopic fluctuations.

Recent results in the literature concerning holography indicate that the thermodynamics of quantum gravity ͑at least with a negative cosmological constant͒ can be modeled by the large N thermodynamics of quantum field theory. We emphasize that this suggests a completely unitary evolution of processes in quantum gravity, including black hole formation and decay, and even more extreme examples involving topology change. As concrete examples which show that this correspondence holds even when the space-time is only locally asymptotically AdS, we compute the thermodynamical phase structure of the AdS-Taub-NUT and AdS-Taubbolt spacetimes, and compare them to a ͑2ϩ1͒-dimensional conformal field theory ͑at large N͒ compactified on a squashed three-sphere and on the twisted plane. ͓S0556-2821͑99͒06302-X͔

We study charged brane-world black holes in the model of Randall and Sundrum in which our universe is viewed as a domain wall in asymptotically anti-de Sitter space. Such black holes can carry two types of "charge", one arising from the bulk Weyl tensor and one from a gauge field trapped on the wall. We use a combination of analytical and numerical techniques to study how these black holes behave in the bulk. It has been shown that a Reissner-Nordstrom geometry is induced on the wall when only Weyl charge is present. However, we show that such solutions exhibit pathological features in the bulk. For more general charged black holes, our results suggest that the extent of the horizon in the fifth dimension is usually less than for an uncharged black hole that has the same mass or the same horizon radius on the wall.