Hamiltonian formulation of Palatini fðRÞ theories à la Brans-Dicke theory
نویسندگان
چکیده
Helios Sanchis-Alepuz Institut für Physik, Karl-Franzens-Universität Graz, Austria (Received 20 December 2010; published 19 May 2011) We study the Hamiltonian formulation of fðRÞ theories of gravity both in metric and in Palatini formalism using their classical equivalence with Brans-Dicke theories with a nontrivial potential. The Palatini case, which corresponds to the ! 1⁄4 3=2 Brans-Dicke theory, requires special attention because of new constraints associated with the scalar field, which is nondynamical. We derive, compare, and discuss the constraints and evolution equations for the ! 1⁄4 3=2 and ! 3=2 cases. Based on the properties of the constraint and evolution equations, we find that, contrary to certain claims in the literature, the Cauchy problem for the ! 1⁄4 3=2 case is well formulated and there is no reason to believe that it is not well posed in general.
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