Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory

Understand

We develop a Hamiltonian formalism of brane-world gravity, which singles out two preferred, mutually orthogonal directions.

• One is a unit twist-free field of spatial vectors with integral lines intersecting perpendicularly the brane.
• The other is a temporal vector field with respect to which we perform the Arnowitt-Deser-Misner decomposition of the Einstein-Hilbert Lagrangian.
• The gravitational variables arise from the projections of the spatial metric and their canonically conjugated momenta as tensorial, vectorial and scalar quantities defined on the family of hypersurfaces containing the brane.