Some theoretical developments in theories beyond General Relativity within the Palatini formalism

In this talk I will focus on some modifications of General Relativity, particularly on the so-called f(R) gravities within the Palatini formalism. I will introduce a reformulation of the variational principle for this class of theories that allows to obtain the corresponding boundary term that should be subtracted in the action to establish a well-posed variational principle. This allows, among other things, to obtain the correct expression for the Black Hole entropy for Schwarzschild spacetimes through the Euclidean semiclassical approach. I will also present the so-called 3+1 decomposition within these theories and the derivation of the corresponding Israel junction conditions.

 

References:

DS-CG, ``Variational principle and boundary terms in gravity à la Palatini,'' Phys. Lett. B 814, 136103 (2021), doi:10.1016/j.physletb.2021.136103 [arXiv:2011.11568 [gr-qc]].