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

Understand

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.