On the on-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries

Abstract

We study a generalization of the Holst action where we admit nonmetricity and torsion in manifolds with timelike boundaries (both in the metric and tetrad formalism). We prove that its space of solutions is equal to the one of the Palatini action. Therefore, we conclude that the metric sector is in fact identical to GR, which is defined by the Einstein-Hilbert action. We further prove that, despite defining the same space of solutions, the Palatini and (the generalized) Holst Lagrangians are not cohomologically equal. Thus, the presymplectic structure and charges provided by the Covariant Phase Space method might differ. However, using the relative bicomplex framework, we show the covariant phase spaces of both theories are equivalent (and in fact equivalent to GR), as well as their charges, clarifying some open problems regarding dual charges and their equivalence in different formulations.

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Cited by in corpus (4)

• Proof of the equivalence of the symplectic forms derived from the canonical and the covariant phase space formalisms
• On the covariant formulation of gauge theories with boundaries
• Asymptotically Safe Hilbert-Palatini Gravity in an On-Shell Reduction Scheme
• On covariant and canonical Hamiltonian formalisms: Weakly Isolated Horizons