Topological black holes in pure Gauss-Bonnet gravity and phase transitions

Abstract

We study charged, static, topological black holes in pure Gauss-Bonnet gravity in asymptotically AdS space. As in general relativity, the theory possesses a unique nondegenerate AdS vacuum. It also admits charged black hole solutions which asymptotically behave as the Reissner-Nordström AdS black hole. We discuss black hole thermodynamics of these black holes. Then we study phase transitions in a dual quantum field theory in four dimensions, with the Stückelberg scalar field as an order parameter. We find in the probe limit that the black hole can develop hair below some critical temperature, which suggests a phase transition. Depending on the scalar coupling constants, the phase transition can be first or second order. Analysis of the free energy reveals that, comparing the two solutions, the hairy state is energetically favorable, thus a phase transition will occur in a dual field theory. *

Null paths on a toroidal topological black hole in conformal Weyl gravity

“…Note from Eqs. (30) and (38) that the module of one trajectory corresponds to the complementary module of the other,…”

“…Other studies associated with topological black holes can be found, for example, in Refs. [29,30], among others. Then we obtain the conserved quantities together with the equations of motion for massless particles on these manifolds.…”

Pure Lovelock gravity and Chern-Simons theory

“…As was pointed out in Ref. [15], the (A)dS space in the PL theory is not directly related to the sign of a cosmological constant like in General Relativity. Indeed, the definition of (A)dS space is due to the sign of curvature R ab = ∓ 1 ℓ 2 e a e b , and not of the explicit Λ, which now has the dimension of the length −2p (at the same time the dimension of the gravitational constant κ is length 2p−D ).…”

“…In the present section we will show how the five-dimensional maximal Pure Lovelock action (the first non trivial example referred also as the Pure Gauss-Bonnet [15,3]) could be obtained from a CS gravity theory for a particular choice of the C m algebra.…”

Lovelock gravities from Born–Infeld gravity theory

“…Those symmetries were introduced in Refs.c [28,29,30,31,32,33,34] and can be regarded as generalizations of the so called Maxwell algebra [35,36], which describes the symmetries of quantum fields in Minkowski space with the presence of a constant electromagnetic field. Thus, for completeness and also due to the growing interest in the effect of higher-curvature terms in the holographic context (see for example [37,38,39,40]), in this work we will show that different Lovelock gravity actions in even dimensions can be obtained from a BI action based on the C m algebra. We shall start by considering the six-dimensional spacetime since it allows us to obtain a bigger variety of gravity theories.…”