Bekenstein bounds in maximally symmetric nonlinear electrodynamics

TL;DR

This paper investigates the properties of ModMax, a maximally symmetric nonlinear extension of electromagnetism, demonstrating well-posedness, geometric inequalities related to Bekenstein bounds, and stable numerical simulations showing birefringence effects.

Contribution

It establishes the well-posedness of ModMax, proves geometric inequalities supporting Bekenstein bounds, and performs the first stable numerical simulations in the nonlinear regime.

Findings

ModMax admits a well-posed initial-value formulation.

Geometric inequalities in ModMax support Bekenstein bounds.

Numerical simulations reveal birefringence and nonlinear effects.

Abstract

We explore dynamical features of the maximally symmetric nonlinear extension of classical electromagnetism, recently proposed in the literature as ``ModMax'' electrodynamics. This family of theories is the only one that preserves all the symmetries of Maxwell's theory, having applications in the study of regular black hole solutions and supersymmetry. The purpose of this article is three-fold. Firstly, we study the initial-value problem of ModMax and show, by means of a simple geometric criterion, that such a theory admits a well-posed formulation. Secondly, we prove a series of geometric inequalities relating energy, charge, angular momentum, and size in ModMax. The validity of these bounds gives strong evidence of an universal inequality conjectured by Bekenstein for macroscopic systems. Finally, we perform the first stable numerical simulations of ModMax in the highly nonlinear regime. We apply our simulations for verifying an inequality between energy, size and angular momentum in bounded domains, and for showing birefringence as a function of the nonlinear parameter, comparing with other nonlinear nonlinear extensions.