Affine Gravity, Palatini Formalism and Charges

TL;DR

This paper develops a covariant method to compute gravitational charges for Lovelock theories, applying it to various scenarios including Bondi energy loss and Einstein-Gauss-Bonnet gravity, confirming known results and deriving new superpotentials.

Contribution

It introduces a covariant formalism for calculating charges in Lovelock gravity, extending previous methods and providing new superpotentials for high-dimensional theories.

Findings

Reproduces standard results for gravitational charges.

Calculates Bondi energy loss in five-dimensional gravity.

Derives superpotentials for Einstein-Gauss-Bonnet and Lovelock theories.

Abstract

Affine gravity and the Palatini formalism contribute both to produce a simple and unique formula for calculating charges at spatial and null infinity for Lovelock type Lagrangians whose variational derivatives do not depend on second-order derivatives of the field components. The method is based on the covariant generalization due to Julia and Silva of the Regge-Teitelboim procedure that was used to define properly the mass in the classical formulation of Einstein's theory of gravity. Numerous applications reproduce standard results obtained by other secure but mostly specialized methods. As a novel application we calculate the Bondi energy loss in five dimensional gravity, based on the asymptotic solution given by Tanabe, Tanahashi and Shiromizu, and obtain, as expected, the same result. We also give the superpotential for Einstein-Gauss-Bonnet gravity and find the superpotential for Lovelock theories of gravity when the number of dimensions tends to infinity with maximally symmetrical boundaries. The paper is written in standard component formalism.