34 research outputs found
Affine Gravity, Palatini Formalism and Charges
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.Comment: The work is dedicated to Joshua Goldberg from whom I learned and got
interested in conservation laws in General Relativity (J.K