Abstract
We show that families of nonlinear gravity theories formulated in a metric-affine approach and coupled to a nonlinear theory of electrodynamics can be mapped into general relativity (GR) coupled to another nonlinear theory of electrodynamics. This allows to generate solutions of the former from those of the latter using purely algebraic transformations. This correspondence is explicitly illustrated with the Eddington-inspired Born–Infeld theory of gravity, for which we consider a family of nonlinear electrodynamics and show that, under the map, preserve their algebraic structure. For the particular case of Maxwell electrodynamics coupled to Born–Infeld gravity we find, via this correspondence, a Born–Infeld-type nonlinear electrodynamics on the GR side. Solving the spherically symmetric electrovacuum case for the latter, we show how the map provides directly the right solutions for the former. This procedure opens a new door to explore astrophysical and cosmological scenarios in nonlinear gravity theories by exploiting the full power of the analytical and numerical methods developed within the framework of GR.
Highlights
In a recent work [14], some of us showed that for Riccibased gravity theories (RBGs) in the metric-affine formulation, there exists a correspondence between the space of solutions of those theories and the space of solutions of general relativity (GR)
To illustrate the method explained in the previous section, here we shall derive the solution for the case of Maxwell electrodynamics coupled to Eddington-inspired Born–Infeld (EiBI) gravity
In this work we have introduced a correspondence between the space of solutions of Ricci-based theories of gravity formulated in the metric-affine approach, and that of General Relativity
Summary
In a recent work [14], some of us showed that for Riccibased gravity theories (RBGs) in the metric-affine formulation (no a priori relation imposed between the metric tensor and the affine connection), there exists a correspondence between the space of solutions of those theories and the space of solutions of GR. Understanding this aspect will shed useful light on some properties of the electrovacuum solutions of the EiBI gravity which were so far not fully understood The existence of this correspondence is useful for the community working on astrophysical and cosmological applications of nonlinear models of matter, specially those in NEDs [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. 3 we identify the particular class of anisotropic fluids electrovacuum fields correspond to, and work out the mapping for the (very general) family of Möbius-type NEDs. In Sect. 3 we identify the particular class of anisotropic fluids electrovacuum fields correspond to, and work out the mapping for the (very general) family of Möbius-type NEDs
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