A connection between linearized Gauss-Bonnet gravity and classical electrodynamics

A connection between linearized Gauss-Bonnet gravity and classical electrodynamics is found by developing a procedure which can be used to derive completely gauge-invariant models. The procedure involves building the most general Lagrangian for a particular order of derivatives (N) and a rank of tensor potential (M), then solving such that the model is completely gauge-invariant (the Lagrangian density, equation of motion and energy-momentum tensor are all gauge-invariant). In the case of N = 1 order of derivatives and M = 1 rank of tensor potential, electrodynamics is uniquely derived from the procedure. In the case of N = 2 order of derivatives and M = 2 rank of symmetric tensor potential, linearized Gauss-Bonnet gravity is uniquely derived from the procedure. The natural outcome of the models for classical electrodynamics and linearized Gauss-Bonnet gravity from a common set of rules provides an interesting connection between two well-explored physical models.