We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing R 5 terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff's Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler's polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in arXiv:1003.4773, the general geometric structure of these Lagrangians remains an open problem.

We show that the semiclassical entropy of D−dimensional rotating (an)isotropic black holes with planar horizon can be successfully computed according to a Cardy-like formula. This formula does not refer to any central charges but instead involves the vacuum energy which is identified with a gravitational bulk soliton. The soliton is obtained from the non-rotating black hole solution by means of a double analytic continuation. The robustness of the Cardy-like formula is tested with numerous and varied examples, including AdS, Lifshitz and hyperscaling violation planar black holes.

In this paper, we construct four-dimensional charged black branes of a nonminimally coupled and self-interacting scalar field. In addition to the scalar and Maxwell fields, the model involves two axionic fields homogeneously distributed along the two-dimensional planar base manifold providing in turn a simple mechanism of momentum dissipation. Interestingly enough, the horizon of the solution can be set at two different positions, whose locations depend on the axionic parameter, and in both cases there exists a wide range of values of the nonminimal coupling parameter yielding physical acceptable solutions. For one of our solutions, the allowed nonminimal coupling parameters take discrete values and it turns out to be extremal since its has zero temperature. A complete analysis of the thermodynamical features of the solutions is also carried out. Finally, thanks to the mechanism of momentum dissipation, the holographic DC conductivities of the solutions are computed in term of the black hole horizon data, and we analyze the effects of the nonminimal coupling parameter on these conductivities. For example, we notice that for the non extremal solutions, there always exists a nonminimal coupling (which is greater than the conformal one in four dimensions) yielding perfect conductivity in the sense that the conductivity is infinite. Even more astonishing, the conductivity matrix for the extremal solutions has a Hall effect-like behavior.

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In this work, we consider the recently proposed well-defined theory that permits a healthy D → 4 limit of the Einstein-Gauss-Bonnet combination, which requires the addition of a scalar degree of freedom. We continue the construction of exact, hairy black hole solutions in this theory in the presence of matter sources, by considering a nonlinear electrodynamics source, constructed through the Plebański tensor and a precise structural function H(P ). Computing the thermodynamic quantities with the Wald formalism, we identify a region in parameter space where the hairy black holes posses well-defined, non-vanishing, finite thermodynamic quantities, in spite of the relaxed asymptotic approach to planar AdS. We test its local stability under thermal and electrical fluctuations and we also show that a Smarr relation is satisfied for these black hole configurations.

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