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arXiv · 2103.16319

3+1 decomposition in modified gravities within the Palatini formalism and some applications

Diego Sáez-Chillón Gómez
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Abstract

In the present paper, the 3+1 decomposition of the spacetime onto hypersurface(s) is analysed and established for theories within the Palatini formalism by considering a general function of the Ricci scalar in the gravitational action. The corresponding Gauss-Codazzi relations are obtained and the boundary term that has to be subtracted in the gravitational action is easily deduced. Then, these relations are applied to the so-called ADM decomposition to describe the foliation of the spacetime onto hypersurfaces of constant time within these theories. Finally, the junction conditions are also obtained by using a decomposition in Gaussian normal coordinates, which coincide with the conditions deduced previously through different approaches.

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Diego Sáez-Chillón Gómez. 2021-03-30. 3+1 decomposition in modified gravities within the Palatini formalism and some applications. https://doi.org/10.1103/physrevd.104.024029

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