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

J.F. Barbero G., J. Margalef-Bentabol, V. Varo, E.J. S. Villaseñor

Physical Review D Vol. 105, nº. 6, pp. 064066

Summary:

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 general relativity (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.

Keywords: First order gravity, Holst action, Boundaries, Covariant Methods

JCR Impact Factor and WoS quartile: 5,000 - Q1 (2022)

DOI reference: https://doi.org/10.1103/PhysRevD.105.064066

Published on paper: March 2022.

Published on-line: March 2022.

Citation:
J.F. Barbero G., J. Margalef-Bentabol, V. Varo, E.J. S. Villaseñor, On-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries. Physical Review D. Vol. 105, nº. 6, pp. 064066, March 2022. [Online: March 2022]