Teorias RBGs com eletrodinâmica não linear por mapeamento à relatividade geral.

Abstract

In the last decades, the discovery of Matter and Dark Energy brought problems to Einstein’s General Relativity (GR), even though it is a very well-established theory. With this, new alternative approaches to this theory have emerged seeking to solve some of these problems. In particular, the theories of gravity based on Ricci, among which stand out the f(R) theories and the Born-Infeld theory inspired by Eddington’s gravity (EiBI), when formulated "à la Palatini", allow to be mapped in General Relativity and vice versa, both at the level of equations and solutions. This fact makes it possible to use very consistent results and methods from General Relativity to explore new results in this extended context of gravitational physics. This procedure has been applied in some cases in the literature. In this work, we focus on EiBI coupled with a nonlinear electrodynamics NED, and show that, with the use of the map, it is possible to relate it to other NEDs coupled to GR. For the particular case of Maxwell’s electrodynamics, we find, through this correspondence, a non-linear Born-Infeld electrodynamics on the General Relativity side. Finally, solving the case of spherically symmetrical vacuum in GR, we show how the map directly provides the right solutions for EiBI. This procedure opens a new door for the study of astrophysical and cosmological scenarios in extended theories of gravity, exploring the full power of the analytical and numerical methods developed within the scope of GR.