Exact solutions for the Einstein-Gauss-Bonnet theory in five dimensions:

G. DOTTI, J. OLIVA Y R. TRONCOSO

PHYSICAL REVIEW D - PARTICLE AND FILDS

American Physical Society

Año: 2007 vol. 76 p. 64038 - 64038

0556-2821

An exhaustive classification of a certain class of static solutions for the five-dimensional Einstein-Gauss-Bonnet theory in vacuum is presented. The class of metrics under consideration is such that thespacelike section is a warped product of the real line with a nontrivial base manifold. It is shown that forgeneric values of the coupling constants the base manifold must be necessarily of constant curvature, andthe solution reduces to the topological extension of the Boulware-Deser metric. It is also shown that thebase manifold admits a wider class of geometries for the special case when the Gauss-Bonnet coupling isproperly tuned in terms of the cosmological and Newton constants. This freedom in the metric at theboundary, which determines the base manifold, allows the existence of three main branches of geometriesin the bulk. For the negative cosmological constant, if the boundary metric is such that the base manifoldis arbitrary, but fixed, the solution describes black holes whose horizon geometry inherits the metric of thebase manifold. If the base manifold possesses a negative constant Ricci scalar, two different kinds ofwormholes in vacuum are obtained. For base manifolds with vanishing Ricci scalar, a different class ofsolutions appears resembling ‘‘spacetime horns.’’ There is also a special case for which, if the basemanifold is of constant curvature, due to a certain class of degeneration of the field equations, the metricadmits an arbitrary redshift function. For wormholes and spacetime horns, there are regions for which thegravitational and centrifugal forces point towards the same direction. All of these solutions have finiteEuclidean action, which reduces to the free energy in the case of black holes, and vanishes in the othercases. The mass is also obtained from a surface integral.