Conserved charges of Einstein gravity in a connection-independent formulation

Abstract

We derive the conserved currents and potentials for Einstein gravity on the basis of a recently proposed connection-independent formulation of this theory. Particularly, we obtain a superpotential that generalizes naturally the usual Katz–Bicak–Lynden–Bell (KBL) one by including the contribution from an arbitrary reference affine connection. The potentials can be adopted to define conserved charges of Einstein gravity. By contrast with the usual metric formulation described by the Einstein–Hilbert Lagrangian, our analysis reveals that the connection-independent formulation conveniently reproduces the KBL superpotential and it can provide a unified description for conserved charges defined by virtue of the KBL method and the covariant phase space approach. In addition, we investigate the properties of the connection-independent Lagrangian under connection and conformal transformations, and we reveal that the connection-independent Lagrangian can be reproduced by converting the Levi-Civita connection in the boundary term into an arbitrary one in terms of the Gamma squared expression for the Einstein–Hilbert Lagrangian.