Conserved currents in the Palatini formulation of general relativity
arXiv:2004.15002 · doi:10.22323/1.376.0171
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.
12 Pages