We consider an action for an abelian gauge field for which the density is given by a power of the Maxwell Lagrangian. In d spacetime dimensions this action is shown to enjoy the conformal invariance if the power is chosen as d/4. We take advantage of this conformal invariance to derive black hole solutions electrically charged with a purely radial electric field. Because of considering power of the Maxwell density, the black hole solutions exist only for dimensions which are multiples of four. The expression of the electric field does not depend on the dimension and corresponds to the four-dimensional Reissner-Nordström field. Using the Hamiltonian action we identify the mass and the electric charge of these black hole solutions.

We show that three-dimensional massive gravity admits Lifshitz metrics with generic values of the dynamical exponent z as exact solutions. At the point z = 3, exact black hole solutions which are asymptotically Lifshitz arise. These spacetimes are three-dimensional analogues of those that were recently proposed as gravity duals for anisotropic scale invariant fixed points.The enormous success of gauge-gravity duality [1] has triggered the interest in generalizing the holographic techniques to other areas of physics. Recently, the attempts to generalize AdS/CFT correspondence to nonrelativistic condensed matter physics have received considerable attention. Besides being an active line of research, this has given raise to very interesting new ideas; see Ref.[2] and references therein for a review.Recently, candidates to be gravity duals for nonrelativistic scale invariant theories, both exhibiting Galilean invariance or not, have been proposed. In Refs. [3,4], spacetimes whose isometry group is the so-called Schrödinger group were proposed to be gravity duals for Galilean and scale invariant systems. In Ref.[5], the scale invariant fixed points that do not exhibit Galilean symmetry were also analyzed, and the metric of the corresponding gravity duals were introduced (see Eq.(2) below). These metrics manifestly exhibit the anisotropic scale invariance

We obtain electrically charged black hole solutions of the Einstein equations in arbitrary dimensions with a nonlinear electrodynamics source. The matter source is deriving from a Lagrangian given by an arbitrary power of the Maxwell invariant. The form of the general solution suggests a natural partition for the different ranges of this power. For a particular range, we exhibit a class of solutions whose behavior resemble to the standard Reissner-Nordström black holes. There also exists a range for which the black hole solutions approach asymptotically the Minkowski spacetime slower than the Schwarzschild spacetime. We have also found a family of not asymptotically flat black hole solutions with an asymptotic behavior growing slower than the Schwarzschild (anti) de Sitter spacetime. In odd dimensions, there exists a critical value of the exponent for which the metric involves a logarithmic dependence. This critical value corresponds to the transition between the standard behavior and the solution decaying to Minkowski slower than the Schwarzschild spacetime.

We study AdS-waves in the three-dimensional new theory of massive gravity recently proposed by Bergshoeff, Hohm, and Townsend. The general configuration of this type is derived and shown to exhibit different branches, with different asymptotic behaviors. In particular, for the special fine tuning m 2 = ±1/(2l 2 ), solutions with logarithmic fall-off arise, while in the range m 2 > −1/(2l 2 ), spacetimes with Schrödinger isometry group are admitted as solutions. Spacetimes that are asymptotically AdS3, both for the Brown-Henneaux and for the weakened boundary conditions, are also identified. The metric function that characterizes the profile of the AdS-wave behaves as a massive excitation on the spacetime, with an effective mass given by m 2 eff = m 2 − 1/(2l 2 ). For the critical value m 2 = −1/(2l 2 ), the value of the effective mass precisely saturates the Breitenlohner-Freedman bound for the AdS3 space where the wave is propagating on. The analogies with the AdS-wave solutions of topologically massive gravity are also discussed. Besides, we consider the coupling of both massive deformations to Einstein gravity and find the exact configurations for the complete theory, discussing all the different branches exhaustively. One of the effects of introducing the Chern-Simons gravitational term is that of breaking the degeneracy in the effective mass of the generic modes of pure New Massive Gravity, producing a fine structure due to parity violation. Another effect is that the zoo of exact logarithmic specimens becomes considerably enlarged. PACS numbers:1 See Ref.[15] for a preliminary derivation of the no-logarithmic branch, where it was argued that in order to be supersymmetric the solutions should not depend on the retarded time. See also Ref. [16], where the interpretation as AdS-waves was first given to the final forms of the metric originally derived in Ref. [13].

We derive electrically charged black hole solutions of the Einstein-Gauss-Bonnet equations with a nonlinear electrodynamics source in n(≥ 5) dimensions. The spacetimes are given as a warped product M 2 × K n−2 , where K n−2 is a (n − 2)-dimensional constant curvature space. We establish a generalized Birkhoff's theorem by showing that it is the unique electrically charged solution with this isometry and for which the orbit of the warp factor on K n−2 is non-null. An extension of the analysis for full Lovelock gravity is also achieved with a particular attention to the Chern-Simons case.

Abstract:We generalize the four-dimensional R 2 -corrected z = 3/2 Lifshitz black hole to a two-parameter family of black hole solutions for any dynamical exponent z and for any dimension D. For a particular relation between the parameters, we find the first example of an extremal Lifshitz black hole. An asymptotically Lifshitz black hole with a logarithmic decay is also exhibited for a specific critical exponent depending on the dimension. We extend this analysis to the more general quadratic curvature corrections for which we present three new families of higher-dimensional D ≥ 5 analytic Lifshitz black holes for generic z. One of these higher-dimensional families contains as critical limits the z = 3 three-dimensional Lifshitz black hole and a new z = 6 four-dimensional black hole. The variety of analytic solutions presented here encourages to explore these gravity models within the context of non-relativistic holographic correspondence.

We consider nonminimally coupled scalar fields to explore the Siklos spacetimes in three dimensions. Their interpretation as exact gravitational waves propagating on AdS restrict the source to behave as a pure radiation field. We show that the related pure radiation constraints single out a unique self-interaction potential depending on one coupling constant. For a vanishing coupling constant, this potential reduces to a mass term with a mass fixed in terms of the nonminimal coupling parameter. This mass dependence allows the existence of several free cases including massless and tachyonic sources. There even exists a particular value of the nonminimal coupling parameter for which the corresponding mass exactly compensates the contribution generated by the negative scalar curvature, producing a genuinely massless field in this curved background. The self-interacting case is studied in detail for the conformal coupling. The resulting gravitational wave is formed by the superposition of the free and the self-interaction contributions, except for a critical value of the coupling constant where a non-perturbative effect relating the strong and weak regimes of the source appears. We establish a correspondence between the scalar source supporting an AdS wave and a pp wave by showing that their respective pure radiation constraints are conformally related, while their involved backgrounds are not. Finally, we consider the AdS waves for topologically massive gravity and its limit to conformal gravity.

We consider an Abelian gauge field coupled to a particular truncation of Horndeski theory. The Galileon field has translation symmetry and couples non minimally both to the metric and the gauge field. When the gauge-scalar coupling is zero the gauge field reduces to a standard Maxwell field. By taking into account the symmetries of the action, we construct charged black hole solutions. Allowing the scalar field to softly break symmetries of spacetime we construct black holes where the scalar field is regular on the black hole event horizon. Some of these solutions can be interpreted as the equivalent of Reissner-Nordstrom black holes of scalar tensor theories with a non trivial scalar field. A self tuning black hole solution found previously is extended to the presence of dyonic charge without affecting whatsoever the self tuning of a large positive cosmological constant. Finally, for a general shift invariant scalar tensor theory we demonstrate that the scalar field Ansatz and method we employ are mathematically compatible with the field equations. This opens up the possibility for novel searches of hairy black holes in a far more general setting of Horndeski theory.