Abstract
A general f(R) gravitational theory is considered within the Palatini formalism. By applying the variational principle and the usual conditions on the boundary, we show explicitly that a surface term remains such that as in their metric-compatible counterparts, an additional surface term has to be added in the gravitational action, which plays a fundamental role when calculating the entropy of the black hole.
Highlights
Gravitational theories are described by the spacetime metric that measures lengths and covariant derivatives which provide the way vectors are parallely transported
Here by assuming Dirichlet boundary conditions on the variations of the compatible metric, the corresponding non-null boundary terms are obtained for the Palatini formalism and we propose a surface counter-term to be added in the gravitational action
We have shown that the surface term corresponding to a theory of gravity formulated in the Palatini formalism can not be removed but provides a contribution similar to the well known GibbonsHawking-York term of General Relativity and other theories including scalar tensor theories [6, 7]
Summary
Diego Saez-Chillon Gomez1, ∗ 1Department of Theoretical Physics, Atomic and Optics, Campus Miguel Delibes, University of Valladolid UVA, Paseo Belen, 7, 47011 - Valladolid, Spain. By applying the variational principle and the usual conditions on the boundary, we show explicitly that a surface term remains such that as in their metric-compatible counterparts, an additional surface term has to be added in the gravitational action, which plays a fundamental role when calculating the entropy of the black hole
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