Static wormhole solution for higher-dimensional gravity in vacuum

G. DOTTI, J. OLIVA Y R. TRONCOSO

PHYSICAL REVIEW D - PARTICLE AND FILDS

American Physical Society

Año: 2007 p. 24002 - 24002

0556-2821

A static wormhole solution for gravity in vacuum is found for odd dimensions greater than four. In fivedimensions the gravitational theory considered is described by the Einstein-Gauss-Bonnet action wherethe coupling of the quadratic term is fixed in terms of the cosmological constant. In higher dimensionsd = 2n + 1, the theory corresponds to a particular case of the Lovelock action containing higher powersof the curvature, so that in general, it can be written as a Chern-Simons form for the AdS group. Thewormhole connects two asymptotically locally AdS spacetimes each with a geometry at the boundarylocally given by R X S1 X H_{d-3}. Gravity pulls towards a fixed hypersurface located at some arbitraryproper distance parallel to the neck. The causal structure shows that both asymptotic regions are connectedby light signals in a finite time. The Euclidean continuation of the wormhole is smooth independently ofthe Euclidean time period, and it can be seen as instanton with vanishing Euclidean action. The mass canalso be obtained from a surface integral and it is shown to vanish.