Static wormholes in vacuum and gravity in diverse dimensions

Abstract

Static wormhole solutions in vacuum for gravity in diverse dimensions are discussed. In dimensions greater than four the theory corresponds to a particular case of the Lovelock action, so that it admits a unique AdS vacuum. One of the wormhole solutions connects two asymptotically locally AdS spacetimes so that both asymptotic regions are connected by light signals in a finite time. The Euclidean continuation of the wormhole can be seen as instanton with vanishing action, and the mass can also be obtained from a surface integral which is shown to vanish. Its stability against free scalar field perturbations is guaranteed provided the squared mass is bounded from below by a negative quantity which could be more stringent than the Breitenlohner-Freedman bound.An exact expression for the spectrum is found analytically. For nonminimal coupling, stability can also be achieved for scalar fields with slow fall-off, and three different quantizations can be carried on, being characterized by the fall-off of the scalar field, which can be fast or slow with respect to each asymptotic region. In four dimensions a static spherically symmetric wormhole solution for conformal gravity in vacuum is found, whose neck connects two static homogeneous universes of constant spatial curvature. Time runs at different rates on each side of the neck. The extension with radial electric or magnetic fields is also discussed and it turns out to have "charge without charge." The solutions can be further generalized to the case of necks with genus greater than one. It is shown that the wormholes in vacuum generically correspond to the matching of different Einstein spacetimes at infinity by means of improper conformal transformations. © Springer Science+Business Media, LLC 2009.