Hamiltonians for Reduced Gravity

TL;DR

This paper introduces a generalized canonical formulation of gravity that maintains n-dimensional covariance, suitable for specific spacetime decompositions, and allows derivation of boundary terms in the Hamiltonian.

Contribution

It develops a new formalism for gravity that is adaptable to various spacetime foliations while preserving covariance and facilitates boundary term calculations.

Findings

Formalism applicable to 2+2 spacetime decompositions

Retains n-dimensional covariance in the Hamiltonian formulation

Enables derivation of boundary contributions in the 3+1 Hamiltonian

Abstract

A generalised canonical formulation of gravity is devised for foliations of spacetime with codimension $n\ge1$. The new formalism retains n-dimensional covariance and is especially suited to 2+2 decompositions of spacetime. It is also possible to use the generalised formalism to obtain boundary contributions to the 3+1 Hamiltonian.