Black hole thermodynamics, conformal couplings, and R 2 terms

Abstract

Lovelock theory provides a tractable model of higher-curvature gravity in which several questions can be studied analytically. This is the reason why, in the last years, this theory has become the favorite arena to study the effects of higher-curvature terms in the context of AdS/CFT correspondence. Lovelock theory also admits extensions that permit to accommodate matter coupled to gravity in a non-minimal way. In this setup, problems such as the backreaction of matter on the black hole geometry can also be solved exactly. In this paper, we study the thermodynamics of black holes in theories of gravity of this type, which include both higher-curvature terms, U(1) gauge fields, and conformal couplings with matter fields in D dimensions. These charged black hole solutions exhibit a backreacting scalar field configuration that is regular everywhere outside and on the horizon, and may exist both in asymptotically flat and asymptotically Anti-de Sitter (AdS) spaces. We work out explicitly the boundary action for this theory, which renders the variational problem well-posed and suffices to regularize the Euclidean action in AdS. We also discuss several interrelated properties of the theory, such as its duality symmetry under field redefinition and how it acts on black holes and gravitational wave solutions.

Black holes in quasi-topological gravity and conformal couplings

“…[17]. As we said, since the matter action (5.1) differs from other higher-curvature couplings considered in the literature [13,16,28,29], the black hole solution we find from (5.4)-(5.5) also differs from the solutions studied in [17,25].…”

“…The mass and electric charged can be obtained by means of the Regge-Teitelboim approach [24], i.e. by finding the variation of the boundary term of the action that renders a well defined variational principle [25], and reading the mass and the electric charge from the terms multiplying the lapse function N (r) and the electric potential at infinity. This yields the following value for the mass 14) where r + is the horizon radius and Vol is the volume of the unit radius constant curvature base manifold with metric g ab .…”

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.…”

“…In order for the present work to be self-contained, we review the theory that consists of scalar matter conformally coupled to gravity through a non-minimal coupling between a real scalar field and the dimensionally extended Euler densities [23,24,31]. This theory can yield second order field equations for both gravity and matter.…”

Validity of Maxwell equal area law for black holes conformally coupled to scalar fields in $$\text {AdS}_5$$ AdS 5 spacetime

“…Furthermore, there exists a similar situation in the exploration of charged AdS hairy black holes [29] of Einstein-Maxwell theory conformally coupled to a scalar field in five dimensions. The model's action has been given by [30][31][32][33] …”