Gauss-Bonnet black holes in AdS spaces

Abstract

We study thermodynamic properties and phase structures of topological black holes in the Einstein theory with a Gauss-Bonnet term and a negative cosmological constant. The event horizon of these topological black holes can be an hypersurface with positive, zero or negative constant curvature. When the horizon is a zero curvature hypersurface, the thermodynamic properties of black holes are completely the same as those of black holes without the Gauss-Bonnet term, although the two black hole solutions are quite different. When the horizon is a negative constant curvature hypersurface, the thermodynamic properties of the Gauss-Bonnet black holes are qualitatively similar to those of black holes without the Gauss-Bonnet term. When the event horizon is a hypersurface with positive constant curvature, we find that the thermodynamic properties and phase structures of black holes drastically depend on the spacetime dimension d and the coefficient of the Gauss-Bonnet term: when d ≥ 6, the properties of black hole are also qualitatively similar to the case without the Gauss-Bonnet term, but when d = 5, a new phase of locally stable small black hole occurs under a critical value of the GaussBonnet coefficient, and beyond the critical value, the black holes are always thermodynamically stable. However, the locally stable small black hole is not globally preferred, instead a thermal anti-de Sitter space is globally preferred. We find that there is a minimal horizon radius, below which the HawkingPage phase transition will not occur since for these black holes the thermal anti de Sitter space is always globally preferred. *

Spacetimes with longitudinal and angular magnetic fields in third order Lovelock gravity

“…[6]. The thermodynamics of the uncharged static spherically black hole solutions has been considered in [7], of solutions with nontrivial topology in [8,9] and of charged solutions in [6,10]. Recently NUT charged black hole solutions of Gauss-Bonnet gravity and Gauss-Bonnet-Maxwell gravity were obtained [11].…”

Braneworld cosmology in (anti)-de Sitter Einstein-Gauss-Bonnet-Maxwell gravity

“…Recently, Cai found a class of topological black holes in D-dimensional Einstein-GB theory with a cosmological constant [22], generalizing an earlier solution due to Boulware and Deser [20]. These solutions were further generalized to a class of charged SAdS and Schwarzschild-de Sitter (SdS) black holes in the Einstein-GB-Maxwell theory, where a non-trivial electromagnetic field is present [23].…”

“…(2.5) as the 'positive-' and 'negative-branch' solutions, respectively. They reduce to the class considered recently by Cai in the charge neutral limit (Q = 0) [22]. We now proceed to consider the motion of a domain wall (three-brane) along a timelike geodesic of the five-dimensional, static background defined by Eqs.…”

Magnetic black holes with higher-order curvature and gauge corrections in even dimensions

“…Secondly, the metric function (3.12) reduces to the solutions obtained by Dotti and Gleiser [19] for C = 0, by Boulware and Deser, and independently by Wheeler [5] for Θ = 0, C = 0, k = 1, and Λ = 0 and by Lorenz-Petzold and independently by Cai for Θ = 0 and C = 0 [10,12]. Lastly, we see that the metric function (3.12) is not well-defined for C = 0 with n = 5 or n = 9.…”

“…The Gauss-Bonnet black-hole solution with Maxwell electric charge was obtained by Wiltshire [9] and has been generalized to the topological case with a cosmological constant [10,11,12]. Indeed, in the low-energy limit of heterotic string theory, the higher-order correction terms appear also for the Maxwell gauge field [3].…”