A connection between linearized Gauss–Bonnet gravity and classical electrodynamics

Abstract

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 ([Formula: see text]) and a rank of tensor potential ([Formula: see text]), 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 [Formula: see text] order of derivatives and [Formula: see text] rank of tensor potential, electrodynamics is uniquely derived from the procedure. In the case of [Formula: see text] order of derivatives and [Formula: see text] 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.