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Register a new userMicrocanonical description of (micro) black holes
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The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g. negative specific heat and loss of unitarity, encountered when the canonical ensemble is used. In this review we present an overview of the weaknesses of the standard thermodynamic description of black holes and show how the microcanonical approach can provide a consistent description of black holes and their Hawking radiation at all energy scales. Our approach is based on viewing the horizon area as yielding the ensemble density at fixed system energy. We then compare the decay rates of black holes in the two different pictures. Our description is particularly relevant for the analysis of micro-black holes whose existence is predicted in models with extra- spatial dimensions.
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We develop the holographic renormalization of AdS_2 gravity systematically. We find that a bulk Maxwell term necessitates a boundary mass term for the gauge field and verify that this unusual term is invariant under gauge transformations that preserve the boundary conditions. We determine the energy-momentum tensor and the central charge, recovering recent results by Hartman and Strominger. We show that our expressions are consistent with dimensional reduction of the AdS_3 energy-momentum tensor and the Brown--Henneaux central charge. As an application of our results we interpret the entropy of AdS_2 black holes as the ground state entropy of a dual CFT.
We study the system formed by a gaz of black holes and strings within a microcanonical formulation. We derive the microcanonical content of the system: entropy, equation of state, number of components N, temperature T and specific heat. The pressure and the specific heat are negative reflecting the gravitational unstability and a non-homogeneous configuration. The asymptotic behaviour of the temperature for large masses emerges as the Hawking temperature of the system (classical or semiclassical phase) in which the classical black hole behaviour dominates, while for small masses (quantum black hole or string behavior) the temperature becomes the string temperature which emerges as the critical temperature of the system. At low masses, a phase transition takes place showing the passage from the classical (black hole) to quantum (string) behaviour. Within a microcanonical field theory formulation, the propagator describing the string-particle-black hole system is derived and from it the interacting four point scattering amplitude of the system is obtained. For high masses it behaves asymptotically as the degeneracy of states of the system (ie duality or crossing symmetry). The microcanonical propagator and partition function are derived from a (Nambu-Goto) formulation of the N-extended objects and the mass spectrum of the black-hole-string system is obtained: for small masses (quantum behaviour) these yield the usual pure string scattering amplitude and string-particle spectrum M_napprox sqrt{n}; for growing mass it pass for all the intermediate states up to the pure black hole behaviour. The different black hole behaviours according to the different mass ranges: classical, semiclassical and quantum or string behaviours are present in the model.
In this note we discuss the application of the Hamilton-Jacobi formalism to the first order description of four dimensional spherically symmetric and static black holes. In particular we show that the prepotential characterizing the flow coincides with the Hamilton principal function associated with the one-dimensional effective Lagrangian. This implies that the prepotential can always be defined, at least locally in the radial variable and in the moduli space, both in the extremal and non-extremal case and allows us to conclude that it is duality invariant. We also give, in this framework, a general definition of the ``Weinhold metric in terms of which a necessary condition for the existence of multiple attractors is given. The Hamilton-Jacobi formalism can be applied both to the restricted phase space where the electromagnetic potentials have been integrated out as well as in the case where the electromagnetic potentials are dualized to scalar fields using the so-called three-dimensional Euclidean approach. We give some examples of application of the formalism, both for the BPS and the non-BPS black holes.
We propose a correspondence between an Anyon Van der Waals fluid and a (2+1) dimensional AdS black hole. Anyons are particles with intermediate statistics that interpolates between a Fermi-Dirac statistics and a Bose-Einstein one. A parameter $alpha$ ($0<alpha<1$) characterizes this intermediate statistics of Anyons. The equation of state for the Anyon Van der Waals fluid shows that it has a quasi Fermi-Dirac statistics for $alpha > alpha_c$, but a quasi Bose-Einstein statistics for $alpha< alpha_c$. By defining a general form of the metric for the (2+1) dimensional AdS black hole and considering the temperature of the black hole to be equal with that of the Anyon Van der Waals fluid, we construct the exact form of the metric for a (2+1) dimensional AdS black hole. The thermodynamic properties of this black hole is consistent with those of the Anyon Van der Waals fluid. For $alpha< alpha_c$, the solution exhibits a quasi Bose-Einstein statistics. For $alpha > alpha_c$ and a range of values of the cosmological constant, there is, however, no event horizon so there is no black hole solution. Thus, for these values of cosmological constants, the AdS Anyon Van der Waals black holes have only quasi Bose-Einstein statistics.
We study rotating global AdS solutions in five-dimensional Einstein gravity coupled to a multiplet complex scalar within a cohomogeneity-1 ansatz. The onset of the gravitational and scalar field superradiant instabilities of the Myers-Perry-AdS black hole mark bifurcation points to black resonators and hairy Myers-Perry-AdS black holes, respectively. These solutions are subject to the other (gravitational or scalar) instability, and result in hairy black resonators which contain both gravitational and scalar hair. The hairy black resonators have smooth zero-horizon limits that we call graviboson stars. In the hairy black resonator and graviboson solutions, multiple scalar components with different frequencies are excited, and hence these are multioscillating solutions. The phase structure of the solutions are examined in the microcanonical ensemble, i.e. at fixed energy and angular momenta. It is found that the entropy of the hairy black resonator is never the largest among them. We also find that hairy black holes with higher scalar wavenumbers are entropically dominant and occupy more of phase space than those of lower wavenumbers.
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