Junction conditions for vacuum solutions in five-dimensional
Einstein-Gauss-Bonnet gravity are studied. We focus on those cases where two
spherically symmetric regions of space-time are joined in such a way that the
induced stress tensor on the junction surface vanishes. So a spherical vacuum
shell, containing no matter, arises as a boundary between two regions of the
space-time. Such solutions are a generalized kind of spherically symmetric
empty space solutions, described by metric functions of the class C0. New
global structures arise with surprising features. In particular, we show that
vacuum spherically symmetric wormholes do exist in this theory. These can be
regarded as gravitational solitons, which connect two asymptotically (Anti)
de-Sitter spaces with different masses and/or different effective cosmological
constants. We prove the existence of both static and dynamical solutions and
discuss their (in)stability under perturbations that preserve the symmetry.
This leads us to discuss a new type of instability that arises in
five-dimensional Lovelock theory of gravity for certain values of the coupling
of the Gauss-Bonnet term.Comment: 9 pages. This is an extended version of the authors' contribution to
the Proceedings of the Marcel Grossmann Meeting, held in Paris, 12-18 July
200