Black holes in quasi-topological gravity and conformal couplings

Abstract

Lovelock theory of gravity provides a tractable model to investigate the effects of higher-curvature terms in the context of AdS/CFT. Yielding second order, ghost-free field equations, this theory represents a minimal setup in which higher-order gravitational couplings in asymptotically Anti-de Sitter (AdS) spaces, including black holes, can be solved analytically. This however has an obvious limitation as in dimensions lower than seven, the contribution from cubic or higher curvature terms is merely topological. Therefore, in order to go beyond quadratic order and study higher terms in AdS 5 analytically, one is compelled to look for other toy models. One such model is the so-called quasi-topological gravity, which, despite being a higher-derivative theory, provides a tractable setup with R 3 and R 4 terms. In this paper, we investigate AdS 5 black holes in quasi-topological gravity. We consider the theory conformally coupled to matter and in presence of Abelian gauge fields. We show that charged black holes in AdS 5 which, in addition, exhibit a backreaction of the matter fields on the geometry can be found explicitly in this theory. These solutions generalize the black hole solution of quasi-topological gravity and exist in a region of the parameter spaces consistent with the constraints coming from causality and other consistency conditions. They have finite conserved charges and exhibit non-trivial thermodynamical properties.

Quintic quasi-topological gravity

“…The properties of holographic superconductors were explored in [53][54][55]. Exact solution containing matter fields were constructed in [56][57][58][59][60] including also scalars conformally coupled to the quasi-topological densities [61]. The thermodynamics in the extended phase space for these theories was studied in [62] and [63].…”

Hairy black holes in cubic quasi-topological gravity

“…In particular, this paper contains a detailed discussion of the five dimensional black hole solutions of this theory, and also discusses the coupling of the scalar field to both the cubic and quartic quasi-topological densities. As a result, there is some overlap between the results we present in sections 2, 4, and 5 and the results of [62]. However there are also many differences: notably, we study AdS vacua for general scalar field configurations, and provide a detailed account of the thermodynamics from the perspective of black hole chemistry.…”

“…Note: As we were finalizing preparation of this manuscript ref. [62] appeared in the literature. In particular, this paper contains a detailed discussion of the five dimensional black hole solutions of this theory, and also discusses the coupling of the scalar field to both the cubic and quartic quasi-topological densities.…”

Microscopic structures and thermal stability of black holes conformally coupled to scalar fields in five dimensions

“…As expected, the theoretical model we are currently interested in, as the generalization of the Lovelock theory, can offer a practical way with matter conformally coupled to gravity and with the back-reaction of the scalar field, i.e. a scalar field conformally coupled to higher-order Euler densities [31,32]. This model as a kind of quasi-topological gravity can be regarded as the most general scalar field/gravity coupling formulation whose field equations are of second order for both gravity and matter.…”