On Junction Conditions in Gravity Theories with Higher Curvature Terms

We discuss the junction conditions in the context of the Randall-Sundrum model with the Gauss-Bonnet interaction. We consider the Z2 symmetric model where the brane is embedded in an AdS5 bulk, as well as a model without Z2 symmetry in which the brane (in this case called by tradition “shell”) separates two metrically different AdS5 regions. We show that the Israel junction conditions across the membrane (that is either a brane or a shell) have to be modified if more general equations than Einstein’s, including higher curvature terms, hold in the bulk, as is likely to be the case in a low energy limit of string theory. We find that the membrane can then no longer be treated in the thin wall approximation. We derive the junction conditions for the Einstein-Gauss-Bonnet theory including second order curvature terms and show that the microphysics of Gauss-Bonnet thick membranes may, in some instances, be simply hidden in a renormalization of Einstein’s constant.