Singular Hypersurfaces in Einstein--Gauss--Bonnet Theory of Gravitation

We present a general formalism for describing singular hypersurfaces in the Einstein theory of gravitation with a Gauss–Bonnet term. The junction conditions are given in a form which is valid for the most general embedding and matter content and for coordinates chosen independently on each side of the hypersurface. The theory is applied to both a time–like and a light–like hypersurface in brane–cosmology.