Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-04-28
JCAP0811:008,2008
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, latex. V2: reference added, major changes in section 3, conclusions partially corrected
Scientific paper
10.1088/1475-7516/2008/11/008
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 there is a class of theories for which the two formalisms are equivalent. This class contains the Palatini version of Lovelock theory, but also more Lagrangians that are not Lovelock, but respect certain symmetries. For the general case, we find that imposing the Levi-Civita connection as an Ansatz, the Palatini formalism is contained within the metric formalism, in the sense that any solution of the former also appears as a solution of the latter, but not necessarily the other way around. Finally we give the conditions the solutions of the metric equations should satisfy in order to solve the Palatini equations.
Bastero-Gil Mar
Borunda Monica
Janssen Bert
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