The Gravitational Hamiltonian in the Presence of Non-Orthogonal Boundaries

TL;DR

This paper extends the Hamiltonian formulation of gravity to cases with non-orthogonal boundaries, deriving new boundary terms and illustrating their implications through specific examples.

Contribution

It introduces a generalized Hamiltonian framework for gravity that accounts for non-orthogonal boundary intersections, expanding previous orthogonal-boundary assumptions.

Findings

Derived new boundary terms for non-orthogonal boundaries.

Calculated the action and Hamiltonian with background subtraction.

Illustrated the approach with two concrete examples.

Abstract

This paper generalizes earlier work on Hamiltonian boundary terms by omitting the requirement that the spacelike hypersurfaces $\Sigma_t$ intersect the timelike boundary $\cal B$ 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.