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

TL;DR

This paper presents new electrically charged black hole solutions in four-dimensional gravity with a conformally coupled scalar field, exploring their properties, thermodynamics, and causal structure in asymptotically AdS spacetimes.

Contribution

It introduces novel black hole solutions with scalar hair and electric charge, analyzing their thermodynamics and causal structure, including cases with negative mass and non-trivial scalar fields.

Findings

Black holes can have negative mass bounded from below.

Entropy does not follow the area law, involving an effective Newton constant.

Thermodynamic bounds relate to cosmic censorship in different frames.

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 non-extremal black hole is analyzed in the grand canonical ensemble. The entropy does not follow the area, 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 selfinteraction, 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.