Generalized Einstein-Maxwell field equations in the Palatini formalism

TL;DR

This paper develops a generalized set of Einstein-Maxwell field equations within the Palatini formalism, incorporating a nonlinear electromagnetic extension through a new function, and introduces a novel method for solving related algebraic equations.

Contribution

It introduces a new framework for Einstein-Maxwell equations in the Palatini formalism with nonlinear electromagnetic coupling and a novel solution method for Ricci tensor algebraic equations.

Findings

Derived generalized Einstein-Maxwell field equations in Palatini formalism.

Established a new method for solving algebraic equations related to the Ricci tensor.

Extended the coupling of gravity with nonlinear electromagnetic fields.

Abstract

We derive a new set of field equations within the framework of the Palatini formalism.These equations are a natural generalization of the Einstein-Maxwell equations which arise by adding a function $\mathcal{F}(\mathcal{Q})$, with $\mathcal{Q}\equiv F^{\alpha\beta}F_{\alpha\beta}$ to the Palatini Lagrangian $f(R,Q)$.The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field.In addition,a new method is introduced to solve the algebraic equation associated to the Ricci tensor.