Covariant phase space for gravity with boundaries: metric vs tetrad formulations

Abstract

We use covariant phase space methods to study the metric and tetrad formulations of General Relativity in a manifold with boundary and compare the results obtained in both approaches. Proving their equivalence has been a long-lasting problem that we solve here by using the cohomological approach provided by the relative bicomplex framework. This setting provides a clean and ambiguity-free way to describe the solution spaces and associated symplectic structures. We also compute several relevant charges in both schemes and show that they are equivalent, as expected.

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Cited by in corpus (10)

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• Finite Charges from the Bulk Action
• Covariant canonical formulations of classical field theories
• Proof of the equivalence of the symplectic forms derived from the canonical and the covariant phase space formalisms
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