Thermodynamics of Rotating Black Holes in Maxwell-Brans-Dicke Theory (original) (raw)
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Slowly Rotating Black Holes in Brans-Dicke-Maxwell Theory
arXiv (Cornell University), 2009
In this paper, we construct a class of (n+1)-dimensional (n ≥ 4) slowly rotating black hole solutions in Brans-Dicke-Maxwell theory with a quadratic potential. These solutions can represent black holes with inner and outer event horizons, an extreme black hole and a naked singularity and they are neither asymptotically flat nor (anti)-de Sitter. We compute the Euclidean action and use it to obtain the conserved and thermodynamics quantities such as entropy, which does not obey the area law. We also compute the angular momentum and the gyromagnetic ratio for these type of black holes where the gyromagnetic ratio is modified in Brans-Dicke theory compared to the Einstein theory.
Physical Review D, 2006
We construct a class of charged rotating solutions in (n + 1)-dimensional Maxwell-Brans-Dicke theory with flat horizon in the presence of a quadratic potential and investigate their properties. These solutions are neither asymptotically flat nor (anti)de Sitter. We find that these solutions can present black brane, with inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We compute the finite Euclidean action through the use of counterterm method, and obtain the conserved and thermodynamic quantities by using the relation between the action and free energy in grand-canonical ensemble. We find that these quantities satisfy the first law of thermodynamics, and the entropy does not follow the area law.
Thermodynamics of Rotating Black Branes in Gauss-Bonnet-Born-Infeld Gravity
Int J Mod Phys D, 2006
Considering both the Gauss-Bonnet and the Born-Infeld terms, which are on similar footing with regard to string corrections on the gravity side and electrodynamic side, we present a new class of rotating solutions in Gauss-Bonnet gravity with kkk rotation parameters in the presence of a nonlinear electromagnetic field. These solutions, which are asymptotically anti-de Sitter in the presence of cosmological constant, may be interpreted as black brane solutions with inner and outer event horizons, an extreme black brane or naked singularity provided the metric parameters are chosen suitably. We calculate the finite action and conserved quantities of the solutions by using the counterterm method, and find that these quantities do not depend on the Gauss-Bonnet parameter. We also compute the temperature, the angular velocities, the electric charge and the electric potential. Then, we calculate the entropy of the black brane through the use of Gibbs-Duhem relation and show that it obeys the area law of entropy. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta and the charge, and show that the conserved and thermodynamic quantities satisfy the first law of thermodynamics. Finally, we perform a stability analysis in both the canonical and grand-canonical ensemble and show that the presence of a nonlinear electromagnetic field has no effect on the stability of the black branes, and they are stable in the whole phase space.
Physical Review D, 2006
We generalize the quasilocal definition of the stress energy tensor of Einstein gravity to the case of third order Lovelock gravity, by introducing the surface terms that make the action welldefined. We also introduce the boundary counterterm that removes the divergences of the action and the conserved quantities of the solutions of third order Lovelock gravity with zero curvature boundary at constant t and r. Then, we compute the charged rotating solutions of this theory in n + 1 dimensions with a complete set of allowed rotation parameters. These charged rotating solutions present black hole solutions with two inner and outer event horizons, extreme black holes or naked singularities provided the parameters of the solutions are chosen suitable. We compute temperature, entropy, charge, electric potential, mass and angular momenta of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We find a Smarr-type formula and perform a stability analysis by computing the heat capacity and the determinant of Hessian matrix of mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that the system is thermally stable. This is commensurate with the fact that there is no Hawking-Page phase transition for black objects with zero curvature horizon.
Thermodynamics of rotating black branes in Einstein–Born–Infeld-dilaton gravity
Journal of Cosmology and Astroparticle Physics, 2007
In this paper, we construct a new class of charged, rotating solutions of (n + 1)dimensional Einstein-Born-Infeld-dilaton gravity with Liouville-type potentials and investigate their properties. These solutions are neither asymptotically flat nor (anti)de Sitter. We find that these solutions can represent black brane, with inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We also compute temperature, entropy, charge, electric potential, mass and angular momentum of the black brane solutions, and show that these quantities satisfy the first law of thermodynamics. We find that the conserved quantities are independent of the Born-Infeld parameter β, while they depend on the dilaton coupling constant α. We also find the total mass of the black brane with infinite boundary as a function of the entropy, the angular momenta and the charge and perform a stability analysis by computing the heat capacity in the canonical ensemble. We find that the system is thermally stable for α ≤ 1 independent of the values of the charge and Born-Infeld parameters, while for α > 1 the system has an unstable phase. In the latter case, the solutions are stable provided α ≤ α max and β ≥ β min , where α max and β min depend on the charge and the dimensionality of the spacetime. That is the solutions are unstable for highly nonlinear electromagnetic field or when the dilaton coupling constant is large.
Structure and thermodynamics of charged nonrotating black holes in higher dimensions
Physical Review D, 2019
We analyze the structural and thermodynamic properties of D-dimensional (D ≥ 4), asymptotically flat or anti-de Sitter, electrically charged black hole solutions, resulting from the minimal coupling of general nonlinear electrodynamics to general relativity. This analysis deals with static spherically symmetric (elementary) configurations with spherical horizons. Our methods are based on the study of the behavior (in vacuum and on the boundary of their domain of definition) of the Lagrangian density functions characterizing the nonlinear electrodynamic models in flat spacetime. These functions are constrained by some admissibility conditions endorsing the physical consistency of the corresponding theories, which are classified in several families, some of them supporting elementary solutions in flat space that are nontopological solitons. This classification induces a similar one for the elementary black hole solutions of the associated gravitating nonlinear electrodynamics, whose geometrical structures are thoroughly explored. A consistent thermodynamic analysis can be developed for the subclass of families whose associated black hole solutions behave asymptotically as the Schwarzschild metric (in the absence of a cosmological term). In these cases we obtain the behavior of the main thermodynamic functions, as well as important finite relations among them. In particular, we find the general equation determining the set of extreme black holes for every model, and a general Smarr formula, valid for the set of elementary black hole solutions of such models. We also consider the one-parameter group of scale transformations, which are symmetries of the field equations of any nonlinear electrodynamics in flat spacetime. These symmetries are respected by the minimal coupling to gravitation and induce representations of the group in the spaces of solutions of the different models, characterized by their thermodynamic functions. Exploiting this fact we find the expression of the equation of state of the set of black hole solutions associated with any model. These results are generalized to asymptotically anti-de Sitter solutions.
Classical and Quantum Gravity, 2014
Thermodynamic potentials relevant to the microcanonical, the canonical and the grand canonical ensembles, associated with rotating black holes in D-dimensions, are analysed and compared. Such black holes are known to be thermodynamically unstable, but the instability is a consequence of a subtle interplay between specific heats and the moments of inertia and it manifests itself differently in the different ensembles. A simple relation between the product of the specific heat and the determinant of the moment of inertia in both the canonical and the grand canonical ensembles is derived. Myers-Perry black holes in arbitrary dimension are studied in detail. All temperature extrema in the microcanonical ensemble are determined and classified. The specific heat and the moment of inertia tensor are evaluated in both the canonical and the grand canonical ensembles in any dimension. All zeros and poles of the specific heats, as a function of the angular momenta, are determined and the eigenvalues of the isentropic moment of inertia tensor are studied and classified. It is further shown that many of the thermodynamic properties of a Myers-Perry black hole in D − 2 dimensions can be obtained from those of a black hole in D dimensions by sending one of the angular momenta to infinity.
Thermodynamics of charged, rotating, and accelerating black holes
Journal of High Energy Physics
We show how to obtain a consistent thermodynamic description of accelerating asymptotically AdS black holes, extending our previous results by including charge and rotation. We find that the key ingredient of consistent thermodynamics is to ensure that the system is not over-constrained by including the possibility of varying the ‘string’ tensions that are responsible for the acceleration of the black hole, yielding a first law of full cohomogeneity. The first law assumes the standard form, with the entropy given by one quarter of the horizon area and other quantities identified by standard methods. In particular we compute the mass in two independent ways: through a Euclidean action calculation and by the method of conformal completion. The ambiguity in the choice of the normalization of the timelike Killing vector can be fixed by explicit coordinate transformation (in the case of rotation) to the standard AdS form or by holographic methods (in the case of charge). This resolves a ...
A Description of Rotating Multicharged Black Holes in terms of Branes and Antibranes
Arxiv preprint arXiv:0709.3891, 2007
We describe rotating multicharge black holes as stacks of intersecting branes and antibranes together with massless gases on them. Assuming the energies of the gases to be equal, we find that their angular momentum parameters, corresponding to black hole rotations, are also equal. The entropy S of this model is given by S = XS sg where S sg is the supergravity entropy. One can obtain X = 1 under an assumption which violates conservation of energy. We show that X = 1 can also be obtained if one assumes that there is only one single gas, which is some sort of superposition of the gases mentioned above, and that the brane tensions are reduced by a factor of four. In this interpretation, energy is conserved and the unusual assumption that energies, not temperatures, of the gases are equal becomes superfluous.
Rotating Black Holes, Complex Geometry, and Thermodynamics, b
Annals of The New York Academy of Sciences, 1991
In recent years the proposal' to relate the Euclidean action of black holes to approximations of certain functional integrals that can be interpreted as thermodynamic partition functions has been developed extensively. In this paper we outline briefly the key points of these developments and extend them to the treatment of stationary geometries, in particular the geometries of rotating black holes. Stationary holes are ostensibly more difficult to handle than static ones, primarily because neither the extrinsic curvature of the stationary constant-time slices nor the corresponding shift vector vanishes, while both do vanish in the case of static geometries. Consequently, as we shall see, there is no real Euclidean metric that represents a rotating black hole. Nevertheless, the hole can be described by a complex geometry that is an extremum of an appropriate real action-we shall call it the thermodynamical action.