The Gravitational Hamiltonian in the Presence of Non-Orthogonal Boundaries

Abstract

This paper generalizes earlier work on Hamiltonian boundary terms by omitting the requirement that the spacelike hypersurfaces ${\Sigma }_t$ intersect the timelike boundary $\mathcal{B}$ orthogonally. The expressions for the action and Hamiltonian are calculated and the required subtraction of a background contribution is discussed. The new features of a Hamiltonian formulation with non-orthogonal boundaries are then illustrated in two examples.

23 pages, 1 figure, LaTeX. The action is altered to include a corner term which results in a different value for the non-orthogonal term. An additional appendix with Euclidean results is included. To appear in Class. Quant. Grav