We extract exact charged black-hole solutions with flat transverse sections in the framework of D-dimensional Maxwell-f (T ) gravity, and we analyze the singularities and horizons based on both torsion and curvature invariants. Interestingly enough, we find that in some particular solution subclasses there appear more singularities in the curvature scalars than in the torsion ones. This difference disappears in the uncharged case, or in the case where f (T ) gravity becomes the usual linear-in-T teleparallel gravity, that is General Relativity. Curvature and torsion invariants behave very differently when matter fields are present, and thus f (R) gravity and f (T ) gravity exhibit different features and cannot be directly re-casted each other.

There is a growing interest in modified gravity theories based on torsion, as these theories exhibit interesting cosmological implications. In this work, inspired by the teleparallel formulation of general relativity, we present its extension to Lovelock gravity known as the most natural extension of general relativity in higher-dimensional space-times. First, we review the teleparallel equivalent of general relativity and Gauss-Bonnet gravity, and then we construct the teleparallel equivalent of Lovelock gravity. In order to achieve this goal we use the vielbein and the connection without imposing the Weitzenböck connection. Then, we extract the teleparallel formulation of the theory by setting the curvature to null.

We present a new family of asymptotically AdS four-dimensional black hole solutions with scalar hair of a gravitating system consisting of a scalar field minimally coupled to gravity with a selfinteracting potential. For a certain profile of the scalar field we solve the Einstein equations and we determine the scalar potential. Thermodynamically we show that there is a critical temperature below which there is a phase transition of a black hole with hyperbolic horizon to the new hairy black hole configuration.

We study exact solutions to Cosmological Topologically Massive Gravity (CTMG) coupled to Topologically Massive Electrodynamics (TME) at special values of the coupling constants. For the particular case of the so called chiral point lµ G = 1, vacuum solutions (with vanishing gauge field) are exhibited. These correspond to a one-parameter deformation of GR solutions, and are continuously connected to the extremal Bañados-Teitelboim-Zanelli black hole (BTZ) with bare constants J = −lM . At the chiral point this extremal BTZ turns out to be massless, and thus it can be regarded as a kind of ground state. Although the solution is not asymptotically AdS3 in the sense of Brown-Henneaux boundary conditions, it does obey the weakened asymptotic recently proposed by Grumiller and Johansson. Consequently, we discuss the holographic computation of the conserved charges in terms of the stress-tensor in the boundary. For the case where the coupling constants satisfy the relation lµ G = 1 + 2lµ E , electrically charged analogues to these solutions exist. These solutions are asymptotically AdS3 in the strongest sense, and correspond to a logarithmic branch of selfdual solutions previously discussed in the literature.