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 ($N$) and 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.

arXiv comment12 pages

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• The general set of Noetherian energy-momentum tensors in linearized gravity: mathematical framework
• Bessel-Hagen currents for the Fierz-Pauli action
• Curvature tensors of higher-spin gauge theories derived from general Lagrangian densities