A connection between linearized Gauss-Bonnet gravity and classical electrodynamics II: Complete dual formulation

Abstract

In a recent publication a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with $N$ order of derivatives and $M$ rank of tensor potential. This procedure was then used to show that unique models follow for each order, namely classical electrodynamics for $N=M=1$ and linearized Gauss-Bonnet gravity for $N=M=2$. In this article, the nature of the connection between these two well explored physical models is further investigated by means of an additional common property; a complete dual formulation. First we give a review of Gauss-Bonnet gravity and the dual formulation of classical electrodynamics. The dual formulation of linearized Gauss-Bonnet gravity is then developed. It is shown that the dual formulation of linearized Gauss-Bonnet gravity is analogous to the homogenous half of Maxwell's theory; both have equations of motion corresponding to the (second) Bianchi identity, built from the dual form of their respective field strength tensors. In order to have a dually symmetric counterpart analogous to the non-homogenous half of Maxwell's theory, the first invariant derived from the procedure in $N=M=2$ can be introduced. The complete gauge invariance of a model with respect to Noether's first theorem, and not just the equation of motion, is a necessary condition for this dual formulation. We show that this result can be generalized to the higher spin gauge theories, where the spin-$n$ curvature tensors for all $N=M=n$ are the field strength tensors for each $n$. These completely gauge invariant models correspond to the Maxwell-like higher spin gauge theories whose equations of motion have been well explored in the literature.

26 pages

References in corpus (24)

• Einstein-Gauss-Bonnet gravity in 4-dimensional space-time
• Electric-Magnetic Duality Rotations in Non-Linear Electrodynamics
• Dual electromagnetism: Helicity, spin, momentum, and angular momentum
• General Gauss-Bonnet brane cosmology
• Charged Black Holes in AdS Spaces in $4D$ Einstein Gauss-Bonnet Gravity
• Introduction to the Classical Theory of Higher Spins
• Free geometric equations for higher spins
• Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
• On geometric equations and duality for free higher spins
• From Gravitons to Gravity: Myths and Reality
• Second Order Scalar Invariants of the Riemann Tensor: Applications to Black Hole Spacetimes
• Gravity from self-interaction redux
• Observational constraints on Gauss-Bonnet cosmology
• String theory triplets and higher-spin curvatures
• Self-Duality in Nonlinear Electromagnetism
• Generalised connections and higher-spin equations
• Manifest Duality for Partially Massless Higher Spins
• Duality rotations in supersymmetric nonlinear electrodynamics revisited
• Late time cosmological scenarios from scalar field with Gauss Bonnet and non-minimal kinetic couplings
• Noether and Hilbert (metric) energy-momentum tensors are not, in general, equivalent
• Mixed-symmetry multiplets and higher-spin curvatures
• Symmetry properties of the metric energy-momentum tensor in classical field theories and gravity
• A connection between linearized Gauss-Bonnet gravity and classical electrodynamics
• The Bianchi identity and weak gravitational lensing

Cited by in corpus (2)

• Canonical Noether and the energy-momentum non-uniqueness problem in linearized gravity
• Curvature tensors of higher-spin gauge theories derived from general Lagrangian densities