Topological black holes dressed with a conformally coupled scalar field and electric charge

Abstract

Electrically charged solutions for gravity with a conformally coupled scalar field are found in four dimensions in the presence of a cosmological constant. If a quartic self-interaction term for the scalar field is considered, there is a solution describing an asymptotically locally AdS charged black hole dressed with a scalar field that is regular on and outside the event horizon, which is a surface of negative constant curvature. This black hole can have negative mass, which is bounded from below for the extremal case, and its causal structure shows that the solution describes a ''black hole inside a black hole''. The thermodynamics of the nonextremal black hole is analyzed in the grand canonical ensemble. The entropy does not follow the area law, and there is an effective Newton constant which depends on the value of the scalar field at the horizon. If the base manifold is locally flat, the solution has no electric charge, and the scalar field has a vanishing stress-energy tensor so that it dresses a locally AdS spacetime with a nut at the origin. In the case of vanishing self interaction, the solutions also dress locally AdS spacetimes, and if the base manifold is of negative constant curvature a massless electrically charged hairy black hole is obtained. The thermodynamics of this black hole is also analyzed. It is found that the bounds for the black holes parameters in the conformal frame obtained from requiring the entropy to be positive are mapped into the ones that guarantee cosmic censorship in the Einstein frame.

Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography

“…Black holes are furthermore thermal backgrounds with calculable thermodynamic or transport quantities. Beyond General Relativity, specific EGTs can admit black holes with primary or secondary hair, permitting non-trivial fields to be switched on in their horizon vicinity, allowing a richer phase structure of solutions for given asymptotic conditions (see for example [45][46][47]). They provide in this sense multiple, regular saddle points in specific thermal baths presenting often phase transitions from non-hairy to hairy black holes as the temperature of the heat bath is lowered.…”

Thermodynamics of charged rotating solutions in Brans–Dicke gravity with Born–Infeld field

“…When a i ¼ 0, the angular momentum vanishes, and so, a i is the ith rotational parameter of the spacetime. Black hole entropy typically satisfies the so-called area law of the entropy [37,38], but it does not follow the area law in Brans-Dicke theory [39][40][41][42][43][44][45]. Nevertheless, the entropy remains invariant under conformal transformations.…”

Static black hole solutions with a self-interacting conformally coupled scalar field

“…A previous four-dimensional and asymptotically flat black hole [7] was reported back in the 70's, but the scalar field diverges at the horizon. The presence of a cosmological constant allows to find exact four-dimensional black hole solutions, where the scalar field is regular on and outside the event horizon [8,9,10,11]. Numerical black hole solutions can also be found in four [12,13,14,15,16] and five dimensions [17].…”

“…(12) below) of spherically symmetric static spacetimes, and are given in equations (13) (14) (solution MTZ1) and (16) (solution MTZ2). Note that a generic spherically symmetric static spacetime metric admits the local form (10). In this work we address the following question: Are there other static, spherically symmetric black hole solutions for the MTZ model, satisfying the dominant and strong energy condition between the event and cosmological horizon, besides MTZ1 and MTZ2?…”