The Palatini formalism for higher-curvature gravity theories

Details The Palatini formalism for higher-curvature gravity theories The Palatini formalism for higher-curvature gravity theories

2009-01-12

arxiv.org/abs/0901.1590v1

Physics

High Energy Physics

High Energy Physics - Theory

4 pages. Contribution to the Spanish Relativity Meeting 2008 in Salamanca, Spain

Scientific paper

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.

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