Black holes in vector-tensor theories and their thermodynamics

In this paper, we study Einstein gravity either minimally or non-minimally coupled to a vector field which breaks the gauge symmetry explicitly in general dimensions. We first consider a minimal theory which is simply the Einstein-Proca theory extended with a quartic self-interaction term for the vector field. We obtain its general static maximally symmetric black hole solution and study the thermodynamics using Wald formalism. The aspects of the solution are much like a Reissner-Nordstr{\o}m black hole in spite of that a global charge cannot be defined for the vector. For non-minimal theories, we obtain a lot of exact black hole solutions, depending on the parameters of the theories. In particular, many of the solutions are general static and have maximal symmetry. However, there are some subtleties and ambiguities in the derivation of the first laws because the existence of an algebraic degree of freedom of the vector in general invalids the Wald entropy formula. The thermodynamics of these solutions deserves further studies.Comment: to appera in EPJC, major revisions, referecens added. 33 page

SU(2)-Colored (A)dS Black Holes in Conformal Gravity

We consider four-dimensional conformal gravity coupled to the U(1) Maxwell and SU(2) Yang-Mills fields. We study the structure of general black hole solutions carrying five independent parameters: the mass, the electric U(1) and magnetic SU(2) charges, the massive spin-2 charge and the thermodynamical pressure associated with the cosmological constant, which is an integration constant in conformal gravity. We derive the thermodynamical first law of the black holes. We obtain some exact solutions including an extremal black hole with vanishing mass and entropy, but with non-trivial SU(2) Yang-Mills charges. We derive the remainder of the first law for this special solution. We also reexamine the colored black holes and derive their first law in Einstein-Yang-Mills gravity with or without a cosmological constant.Comment: Latex, 22 pages, typos corrected and references adde

Exact formation of hairy planar black holes

We consider Einstein gravity minimally coupled to a scalar field with a given potential in general dimensions. We obtain large classes of static hairy planar black holes which are asymptotic to AdS space-times. In particular, for a special case $\mu=(n-2)/2$, we obtain new classes of exact dynamical solutions describing black holes formation. We find there are two classes of collapse solutions. The first class solutions describe the evolution start from AdS space-time with a naked singularity at the origin. The space-time is linearly unstable and evolves into stationary black hole states even under small perturbation. The second class solutions describe the space-time spontaneously evolves from AdS vacua into stationary black hole states undergoing non-linear instability. We also discuss the global properties of all these dynamical solutions.Comment: 17 pages and 5 figures; the general case was studied analytically; conclusions unchange

Charged Black Holes with Scalar Hair

We consider a class of Einstein-Maxwell-Dilaton theories, in which the dilaton coupling to the Maxwell field is not the usual single exponential function, but one with a stationary point. The theories admit two charged black holes: one is the Reissner-Nordstr{\o}m (RN) black hole and the other has a varying dilaton. For a given charge, the new black hole in the extremal limit has the same AdS$_2\times$Sphere near-horizon geometry as the RN black hole, but it carries larger mass. We then introduce some scalar potentials and obtain exact charged AdS black holes. We also generalize the results to black $p$-branes with scalar hair.Comment: Latex, 22 pages, typos corrected and references added, to appear in JHE