On A Covariant Hamiltonian Description of Palatini's Gravity on Manifolds with Boundary

TL;DR

This paper develops a covariant Hamiltonian framework for Palatini's gravity on manifolds with boundary, enabling analysis of topologically non-trivial situations and boundary data in a gauge-theoretic setting.

Contribution

It introduces a multisymplectic approach to Palatini's gravity, extending covariant Hamiltonian methods to manifolds with boundary and topological considerations.

Findings

Reduced phase space is a symplectic manifold.

Boundary data form a distinguished isotropic submanifold.

Framework accommodates non-trivial topological configurations.

Abstract

A covariant Hamiltonian description of Palatini's gravity on manifolds with boundary is presented. Palatini's gravity appears as a gauge theory satisfying a constraint in a certain topological limit. This approach allows the consideration of non-trivial topological situations. The multisymplectic framework for first-order covariant Hamiltonian field theories on manifolds with boundary, developed in [Ib15], enables analysis of the system at the boundary. The reduced phase space of the system is determined to be a symplectic manifold with a distinguished isotropic submanifold corresponding to the boundary data of the solutions of the Euler-Lagrange equations.