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 the vacuum static wormhole, the black hole, and generalized Bertotti-Robinson space-times with nontrivial torsion. All of the solutions have a cross product structure of the type ${M}_{5}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\Sigma}}_{3}$, where ${M}_{5}$ is a five-dimensional manifold and ${\ensuremath{\Sigma}}_{3}$ 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.