LIMA JUNIOR, J. G.; http://lattes.cnpq.br/3032676282436051; LIMA JÚNIOR, José Grimário de.
Resumen:
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.