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

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.

12 pages, version published in PRD

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• ADM formulation and Hamiltonian analysis of $f(Q)$ gravity
• Palatini $R^2$ Quintessential Inflation
• Implications of Palatini gravity for inflation and beyond
• The $3+1$ Formalism in the Geometric Trinity of Gravity
• Junction conditions for generalized hybrid metric-Palatini gravity with applications
• Boundary Conditions for Constraint Systems in Variational Principle
• On the well-posed variational principle in degenerate point particle systems using embeddings of the symplectic manifold
• Dualized Gravity beyond Linear Approximation
• Cosmic inflation in metric-affine gravity
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity