Conserved currents in the Palatini formulation of general relativity

Abstract

We derive the expressions for the local, on-shell closed co-dimension 2 forms in the Palatini formulation of general relativity and explicitly show their on-shell equivalence to those of the metric formulation. When compared to other first order formulations, two subtleties have to be addressed during the construction: off-shell non-metricity and the fact that the transformation of the connection under infinitesimal diffeomorphisms involves second order derivatives of the associated vector fields.

The Weyl BMS group and Einstein’s equations

“…This leads to internal Lorentz charges that are absent in the metric formalism, and a priori different covariant phase spaces. The differences show up for instance in the formulas for the quasi-local charges, which been investigated in [81,113] and [38][39][40]; see also [107,[114][115][116][117] for previous related work. It is known that equivalence of the charges can be restored for isometries using the Kosmann derivative [114][115][116] (see discussion in [81]), but for asymptotic symmetries is it not always the case [111,112]: at null infinity the standard charges are the same but not the dual ones, thus offering a set-up to recover known BMS results, while at the same time accessing the dual sector.…”

“…The differences show up for instance in the formulas for the quasi-local charges, which been investigated in [81,113] and [38][39][40]; see also [107,[114][115][116][117] for previous related work. It is known that equivalence of the charges can be restored for isometries using the Kosmann derivative [114][115][116] (see discussion in [81]), but for asymptotic symmetries is it not always the case [111,112]: at null infinity the standard charges are the same but not the dual ones, thus offering a set-up to recover known BMS results, while at the same time accessing the dual sector. The exact equivalence can be obtained for all charges including arbitrary diffeomorphisms if one works with a dressed symplectic potential [81,113] (see also [87,118]).…”

Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables

“…The present paper attempts to unify and expand certain aspects of previous works [17][18][19][20][21][22][23][24][25][26][27] dealing with metric-Palatini and tetrad-Palatini, focusing on the comparison of both formulations and the treatment of boundaries. In this regard, we would like to highlight the pioneering work by Obukhov [28], where he introduced the appropriate surface terms for Palatini gravity.…”

Conservation and integrability in lower-dimensional gravity

“…For related works in other formalisms see e.g. [24,[67][68][69][70][71][72][73][74][75][76][77][78][79][80][81]. Note that it is expected that different formalisms lead to different symmetry algebras [77].…”