Vacuum static compactified wormholes in eight-dimensional Lovelock theory

Abstract

In this paper new exact solutions in eight dimensional Lovelock theory will be presented. These solutions are vacuum static wormhole, black hole and generalized Bertotti-Robinson space-times with nontrivial torsion. All the solutions have a cross product structure of the type M 5 × Σ 3 where M 5 is a five dimensional manifold and Σ 3 a compact constant curvature manifold. The wormhole is the first example of a smooth vacuum static Lovelock wormhole which is neither Chern-Simons nor Born-Infeld. It will be also discussed how the presence of torsion affects the "navigableness" of the wormhole for scalar and spinning particles. It will be shown that the wormhole with torsion may act as "geometrical filter": a very large torsion may "increase the traversability" for scalars while acting as a "polarizator" on spinning particles. This may have interesting phenomenological consequences.

BTZ-like black holes in even dimensional Lovelock theories

“…(25): see, for instance, [16] and [21]. Interestingly enough, as it will be explained in more details in the next section, the geodesics of the metric in Eq.…”

“…On the other hand, being the torsion fully anti-symmetric, the corresponding contorsion tensor does not affect directly the geodesic equation: see, for instance, [21]. However, the dynamics of Fermions is affected by the presence of torsion: the contorsion tensor directly enters the Dirac equation modifying the spin connection in a way very similar to a "spin-spin" coupling in which the contorsion plays the role of "spin" of the gravitational background.…”

“…(36) which are closed due to only the Bianchi identities for a generic vacuum solution with torsion of Lovelock theories and not just for the class of metrics in Eq. (21). Because of the scarcity of exact solutions with torsion in Lovelock theories, this task seems to be quite difficult but it certainly deserves further investigation.…”

“…(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).…”

“…So it is natural to ask if there exist black hole solutions with torsion in the cases in which no enhanced symmetry is present. An interesting possibility explored in [21] is to consider a eight-dimensional metric which represents a five-dimensional black hole with three compact extra dimensions: in this case the metric supports a non-vanishing torsion flux. Instead here we will construct a genuine eight-dimensional black hole with non-zero torsion along the M 3 × N 3 base manifold.…”