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We explore the properties of a new Maxwell electrodynamics coupled to aLorentz-violating background through the presence of higher-derivative terms.Physical implications of this alternative effective theory modified byLorentz-violating operators of mass dimension-$5$ are considered, such asmodified dispersion relations which exhibit the vacuum birefringencephenomenon. Subsequently, we analyze the energy-momentum tensor in the case wereproduce the Gambini-Pullin electrodynamics. We explicitly show that for abackground time-like four-vector, $n^{\mu}$, the equations of motion indeedreproduce those encountered by Gambini and Pullin in the framework of loopquantum gravity . Finally, extended expressions for Maxwell-type equations arewritten down in the case the external Lorentz-violating four-vector isspace-like.

On a Gambini-Pullin-inspired Maxwell electrodynamics with Lorentz-violating dimension-$5$ operators