Generalized Einstein-Maxwell field equations in the Palatini formalism

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.

arXiv comment4 pages

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Cited by in corpus (1)

• Comparing metric and Palatini approaches to vector Horndeski theory