Israel conditions for the Gauss–Bonnet theory and the Friedmann equation on the brane universe

Assuming an Einstein–Gauss–Bonnet theory of gravitation in a (D⩾5)-dimensional spacetime with boundary, we consider the problem of the boundary dynamics given the matter Lagrangian on it. The resulting equation is applied, in particular, on the derivation of the Friedmann equation of a 3-brane, understood as the non-orientable boundary of a 5d spacetime. We briefly discuss the contradictory conclusions of the literature.