Mokhtar Hassaine

Lifshitz Black Hole in Three Dimensions

We show that three-dimensional massive gravity admits Lifshitz metrics with generic values of the dynamical exponent

Lovelock black holes with a nonlinear Maxwell field

z

Analytic Lifshitz black holes in higher dimensions

as exact solutions. At the point

Bending AdS waves with new massive gravity

z=3

Charged Galileon black holes

, exact black hole solutions that 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.

Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert lagrangian

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 Birkhoffs 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.

Lifshitz black holes with a time-dependent scalar field in a Horndeski theory

We generalize the four-dimensional R2-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.

First law and anisotropic Cardy formula for three-dimensional Lifshitz black holes

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 m2 = ±1/(2l2), solutions with logarithmic fall-off arise, while in the range -1/(2l^2)

Quintic quasi-topological gravity

>m2 > −1/(2l2), spacetimes with Schrodinger 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 meff2 = m2−1/(2l2). For the critical value m2 = −1/(2l2), 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.

Topological black holes for Einstein-Gauss-Bonnet gravity with a nonminimal scalar field

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.