The Palatini formalism for higher-curvature gravity theories
High Energy Physics - Theory
2018-10-18 v1
Abstract
We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that in general the two formalisms are not equivalent and that the set of solutions of the Palatini equations is a non-trivial subset of the solutions of the metric equations. However we also argue that for Lovelock gravities, the equivalence of the two formalism holds completely and give an explanation of why it holds precisely for these theories.
Keywords
Cite
@article{arxiv.0901.1590,
title = {The Palatini formalism for higher-curvature gravity theories},
author = {Mar Bastero-Gil and Monica Borunda and Bert Janssen},
journal= {arXiv preprint arXiv:0901.1590},
year = {2018}
}
Comments
4 pages. Contribution to the Spanish Relativity Meeting 2008 in Salamanca, Spain