Brane-World charges

TL;DR

This paper develops a method to define and compute local gravitational energy and momentum densities in Brane-World models, extending previous Hamiltonian approaches to higher-dimensional scenarios.

Contribution

It introduces a covariant Hamiltonian framework for calculating Brane-World charges, utilizing Lanczos-Israel boundary conditions and applying it to specific examples.

Findings

Successful computation of Brane-World energy and momentum densities.

Extension of Hamiltonian methods to five-dimensional Brane-World scenarios.

Application to simple models demonstrating the approach.

Abstract

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 explicitely covariant generalization of the Hamiltonian procedure of Regge and Teitelboim given in a previous work. We finally study two simple Brane-World examples.