Gauss-Bonnet gravity renders negative tension braneworlds unstable

We show that the addition of the Gauss-Bonnet term to Einstein gravity induces a tachyon mode in the spin two fluctuations of the Randall-Sundrum I model. We demonstrate that this instability is generically related to the presence of a flat negative tension brane, of codimension one, embedded in an anti-de Sitter background. In particular its presence is independent of Z(2)-symmetry or compactness of the extra dimension. The gravitational tachyon mode persists for arbitrarily small but nonvanishing Gauss-Bonnet coupling. It is a bound state localized on the negative tension brane, much like the graviton zero-mode is localized on a positive tension one. We discuss the possible resolution of this instability by the inclusion of induced gravity terms on the branes or by an effective four-dimensional cosmological constant.