Generalized Einstein-Maxwell field equations in the Palatini formalism

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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 F(Q), with Q≡ FαβFαᵦ 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.