  The classification of certain class of static solutions for the
Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of
the class of metrics under consideration is a warped product of the real line
with a nontrivial base manifold. For arbitrary values of the Gauss-Bonnet
coupling, the base manifold must be Einstein with an additional scalar
restriction. The geometry of the boundary can be relaxed only when the
Gauss-Bonnet coupling is related with the cosmological and Newton constants, so
that the theory admits a unique maximally symmetric solution. This additional
freedom in the boundary metric allows the existence of three main branches of
geometries in the bulk, containing new black holes and wormholes in vacuum.
