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.

References in corpus (11)

• Quantum gravity in terms of topological observables
• Topological Interpretation of Barbero-Immirzi Parameter
• Canonical Gravity with Fermions
• Geometric formulation of the Covariant Phase Space methods with boundaries
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
• Surface terms, Asymptotics and Thermodynamics of the Holst Action
• Laws of Black Hole Mechanics from Holst Action
• Covariant phase space for gravity with boundaries: metric vs tetrad formulations
• Concise symplectic formulation for tetrad gravity
• Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action
• Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables

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