Brane-world charges

As opposed to usual Einstein gravity in four dimensions, the brane-world scenario allows the construction of a local density of gravitational energy (and also of momentum of angular momentum, etc). This is a direct consequence of the hypothesis that our universe is located at the boundary of a five-dimensional diffeomorphism invariant manifold. We compute these brane-world densities of charge using the Lanczos-Israel boundary conditions. To proceed, we implement an explicitly covariant generalization of the Hamiltonian procedure of Regge and Teitelboim given in a previous work. Finally, we study two simple brane-world examples.