In this paper we construct asymptotically locally AdS and flat black holes in the presence of a scalar field whose kinetic term is constructed out from a linear combination of the metric and the Einstein tensor. The field equations as well as the energy-momentum tensor are second order in the metric and the field, therefore the theory belongs to the ones defined by Horndeski. We show that in the presence of a cosmological term in the action, it is possible to have a real scalar field in the region outside the event horizon. The solutions are characterized by a single integration constant, the scalar field vanishes at the horizon and it contributes to the effective cosmological constant at infinity. We extend these results to the topological case. The solution is disconnected from the maximally symmetric AdS background, however, within this family there exists a gravitational soliton which is everywhere regular. This soliton is therefore used as a background to define a finite Euclidean action and to obtain the thermodynamics of the black holes. For a certain region in the space of parameters, the thermodynamic analysis reveals a critical temperature at which a Hawking-Page phase transition between the black hole and the soliton occurs. We extend the solution to arbitrary dimensions greater than 4 and show that the presence of a cosmological term in the action allows one to consider the case in which the standard kinetic term for the scalar it is not present. In such a scenario, the solution reduces to an asymptotically flat black hole.

We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing \( {\mathrm{\mathcal{R}}}^5 \) 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 construct new black brane solutions in the context of Horndeski gravity, in particular, in its K-essence sector. These models are supported by axion scalar fields that depend only on the horizon coordinates. The dynamics of these fields is determined by a K-essence term that includes the standard kinetic term $X$ and a correction of the form $X^k$. We find both neutral and charged exact and analytic solutions in $D$-dimensions, which are asymptotically anti–de Sitter. Then, we describe in detail the thermodynamical properties of the four-dimensional solutions and we compute the dual holographic DC conductivity.

We consider a particular truncation of the generalized Proca field theory in four dimensions for which we construct static and axisymmetric rotating black hole “stealth solutions,” namely solutions with (anti) de Sitter or Kerr metric but nontrivial vector field. The static configuration is promoted to a backreacting black hole with asymptotic (anti) de Sitter behavior by turning on a nonlinear electrodynamic source given as a fixed power of the Maxwell invariant. Finally we extend our solutions to arbitrary dimensions.

In this paper we extend the quasitopological electromagnetism, recently introduced by H.-S. Liu et al. [arXiv:1907.10876], to arbitrary dimensions by introducing a fundamental $p$-form field. This allows us to construct new dyonic black hole solutions in odd dimensions, as well as regular $D$-dimensional black holes and solitons. The three-dimensional system consists of a Maxwell field interacting with a scalar field, leading to a deformation of the Bañados-Teitelboim-Zanelli black hole. We present the general formulas defining the black hole solutions in arbitrary dimensions in Lovelock theory and explore the thermal properties of the asymptotically anti–de Sitter black holes in the gravitational framework of general relativity. In five dimensions, the latter black holes possess a rich phase space structure in the canonical ensemble, giving rise to as many as five different black hole phases at a fixed temperature, for a given range of the parameters.

Einstein-Maxwell theory conformally coupled to a scalar field in $D$ dimensions may exhibit a phase transition at low temperature whose end point is an asymptotically anti–de Sitter black hole with a scalar field profile that is regular everywhere outside and on the horizon. This provides a tractable model to study the phase transition of hairy black holes in anti–de Sitter space in which the backreaction on the geometry can be solved analytically.