Non-linear electrodynamics non-minimally coupled to gravity:symmetric-hyperbolicity and causal structure

TL;DR

This paper investigates the conditions for well-posedness and causality in non-linear electrodynamics coupled to gravity, deriving inequalities that constrain field intensities and curvature effects, with implications for the theory's physical viability.

Contribution

It derives general symmetric hyperbolicity conditions for non-linear electrodynamics coupled to gravity, providing new constraints on field and curvature parameters.

Findings

Non-linearity constrains electromagnetic field intensities.

Non-minimal coupling imposes restrictions on curvature-related quantities.

Symmetric hyperbolicity conditions ensure well-posedness of the theory.

Abstract

It is shown here that symmetric hyperbolicity, which guarantees well-posedness, leads to a set of two inequalities for matrices whose elements are determined by a given theory. As a part of the calculation, carried out in a mostly-covariant formalism, the general form for the symmetrizer, valid for a general Lagrangian theory, was obtained. When applied to nonlinear electromagnetism linearly coupled to curvature, the inequalities lead to strong constraints on the relevant quantities, which were illustrated with applications to particular cases. The examples show that non-linearity leads to constraints on the field intensities, and non-minimal coupling imposes restrictions on quantities associated to curvature.