Some exact solutions with torsion in 5D Einstein-Gauss-Bonnet gravity

Abstract

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.

BTZ-like black holes in even dimensional Lovelock theories

“…When the torsion lives on a three-dimensional sub-manifold, it can be proportional to the three-dimensional completely antisymmetric tensor whose properties imply that most of the consistency conditions are automatically satisfied. This ansatz, proposed for the first time in [16], allowed to find the first exact vacuum solutions with non-vanishing torsion in a five-dimensional Lovelock theory without enhanced gauge symmetry 1 [19]. For a five-dimensional black hole metric, such ansatz for torsion turns out to be consistent in the CS case [20].…”

“…(25)). This idea allowed to construct the first exact vacuum solutions with non-trivial torsion in Lovelock gravities [19] [20] [21]. In particular, it has been shown in [19] that using the proposed ansatz for the torsion it is possible to construct a class of black hole solutions in five dimensional Chern-Simons supergravity with a ground state which preserves half of the supersymmetries (something which, without torsion is known to be impossible).…”

“…This idea allowed to construct the first exact vacuum solutions with non-trivial torsion in Lovelock gravities [19] [20] [21]. In particular, it has been shown in [19] that using the proposed ansatz for the torsion it is possible to construct a class of black hole solutions in five dimensional Chern-Simons supergravity with a ground state which preserves half of the supersymmetries (something which, without torsion is known to be impossible). Therefore, being the torsion necessary in order to achieve a half-BPS black-hole solution, it is quite natural to expect that it should be possible to construct with torsion a topological charge (namely, a charge which is constructed using the Bianchi identities but without using the equations of motion or the symmetries of the solution) which enters some sort of BPS bound as in Eq.…”

Vacuum static compactified wormholes in eight-dimensional Lovelock theory

“…However, the "torsion" constants δ (1) and K 2 cannot be rescaled away, they can take any real values (compatible with the equations of motion) since they are true integration constants representing the strength of the torsion in the i and the a directions. Thus, as in [6], the presence of torsion will be manifest directly in the metric: this is unlike the five-dimensional Chern-Simons case in which in the half BPS black hole constructed in [7], torsion manifests itself mainly in the Killing spinor equation.…”

“…In the generic non-Chern-Simons Lovelock case, the equations of motions for the torsion are very restrictive and until very recently, no exact solution with torsion was known. The first was discovered in [6] using the ansatz for the torsion (inspired by an analogy with gauge theory first proposed in [5])…”