The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein-Hilbert term with cosmological constant, the gravitational sector contains the Lorentz-Chern-Simons form and a term involving the torsion each with arbitrary couplings. The supersymmetric extension is carried out for vanishing and negative effective cosmological constant, and it is shown that the action can be written as a Chern-Simons theory for the supersymmetric extension of the Poincare and AdS groups, respectively. Here we introduce a duality map between different gravity theories that greatly simplifies the construction. This map relies on the different ways to make geometry emerge from a single gauge potential. The extension for N = p + q gravitini is also performed. *

In this paper we study dynamical compactification in Einstein-Gauss-Bonnet gravity from an arbitrary dimension for generic values of the coupling constants. We show that, when the curvature of the extra-dimensional space is negative, for any value of the spatial curvature of the four-dimensional space-time one obtains a realistic behavior in which for asymptotic time both the volume of the extra dimension and expansion rate of the four-dimensional space-time tend to a constant. Remarkably, this scenario appears within the open region of parameters space for which the theory does not admit any maximally symmetric (4 þ D)-dimensional solution, which gives to the dynamical compactification an interpretation as geometric frustration. In particular there is no need to fine-tune the coupling constants of the theory so that the present scenario does not violate the ''naturalness hypothesis.'' Moreover we show that with an increase of the number of extra dimensions the stability properties of the solution are increased.

In this paper we perform a systematic classification of the regimes of cosmological dynamics in Einstein-Gauss-Bonnet gravity with generic values of the coupling constants. We consider a manifold which is a warped product of a four dimensional Friedmann-Robertson-Walker space-time with a D-dimensional Euclidean compact constant curvature space with two independent scale factors. A numerical analysis of the time evolution as function of the coupling constants and of the curvatures of the spatial section and of the extra dimension is performed. We describe the distribution of the regimes over the initial conditions space and the coupling constants. The analysis is performed for two values of the number of extra dimensions (D 6 both) which allows us to describe the effect of the number of the extra dimensions as well.

We consider various models of three-dimensional gravity with torsion or nonmetricity (metric affine gravity), and show that they can be written as Chern-Simons theories with suitable gauge groups. Using the groups ISO(2, 1), SL(2, C) or SL(2, R) × SL(2, R), and the fact that they admit two independent coupling constants, we obtain the Mielke-Baekler model for zero, positive or negative effective cosmological constant respectively. Choosing SO(3, 2) as gauge group, one gets a generalization of conformal gravity that has zero torsion and only the trace part of the nonmetricity. This characterizes a Weyl structure. Finally, we present a new topological model of metric affine gravity in three dimensions arising from an SL(4, R) Chern-Simons theory.

Exact vacuum solutions with a nontrivial torsion for the Einstein-Gauss-Bonnet theory in five dimensions are constructed. We consider a class of static metrics whose spacelike section is a warped product of the real line with a nontrivial base manifold endowed with a fully antisymmetric torsion. It is shown requiring solutions of this sort to exist, fixes the Gauss-Bonnet coupling such that the Lagrangian can be written as a Chern-Simons form. The metric describes black holes with an arbitrary, but fixed, base manifold. It is shown that requiring its ground state to possess unbroken supersymmetries, fixes the base manifold to be locally a parallelized threesphere. The ground state turns out to be half-BPS, which could not be achieved in the absence of torsion in vacuum. The Killing spinors are explicitly found.

Motivated by the recently found 4-dimensional ω-deformed gauged supergravity, we investigate the black hole solutions within the single scalar field consistent truncations of this theory. We construct black hole solutions that have spherical, toroidal, and hyperbolic horizon topology. The scalar field is regular everywhere outside the curvature singularity and the stress-energy tensor satisfies the null energy condition. When the parameter ω does not vanish, there is a degeneracy in the spectrum of black hole solutions for boundary conditions that preserve the asymptotic Anti-de Sitter symmetries. These boundary conditions correspond to multi-trace deformations in the dual field theory.

Exact solutions with torsion in Einstein-Gauss-Bonnet gravity are derived. These solutions have a cross product structure of two constant curvature manifolds. The equations of motion give a relation for the coupling constants of the theory in order to have solutions with nontrivial torsion. This relation is not the Chern-Simons combination. One of the solutions has a AdS 2 × S 3 structure and is so the purely gravitational analogue of the Bertotti-Robinson space-time where the torsion can be seen as the dual of the covariantly constant electromagnetic field.

In this paper the generalization of the Gribov pendulum equation in the Coulomb gauge for curved spacetimes is analyzed on static spherically symmetric backgrounds. A rigorous argument for the existence and uniqueness of solution is provided in the asymptotically AdS case. The analysis of the strong and weak boundary conditions is equivalent to analyzing an effective one-dimensional Schrodinger equation. Necessary conditions in order for spherically symmetric backgrounds to admit solutions of the Gribov pendulum equation representing copies of the vacuum satisfying the strong boundary conditions are given. It is shown that asymptotically flat backgrounds do not support solutions of the Gribov pendulum equation of this type, while on asymptotically AdS backgrounds such ambiguities can appear. Some physical consequences are discussed.Comment: 22 pages, no figures. V2: The discussion of the physical consequences has been extended. To appear on Physical Review