Bekenstein Inequalities and Nonlinear Electrodynamics

TL;DR

This paper examines the validity of Bekenstein inequalities within nonlinear electrodynamics, specifically showing Born-Infeld theory satisfies these bounds and exploring their physical implications and connection to causality.

Contribution

It extends the analysis of Bekenstein inequalities from linear to nonlinear electrodynamics, demonstrating Born-Infeld theory satisfies these bounds and analyzing their physical significance.

Findings

Born-Infeld electrodynamics satisfies Bekenstein inequalities.

No rigidity statement exists in Born-Infeld theory.

The inequalities relate to causality and physical bounds.

Abstract

Bekenstein and Mayo proposed a generalised bound for the entropy, which implies some inequalities between the charge, energy, angular momentum, and the size of the macroscopic system. Dain has shown that Maxwell's electrodynamics satisfies all three inequalities. We investigate the validity of these relations in the context of nonlinear electrodynamics and show that Born-Infeld electrodynamics satisfies all of them. However, contrary to the linear theory, there is no rigidity statement in Born-Infeld. We study the physical meaning and the relationship between these inequalities and, in particular, we analyse the connection between the energy-angular momentum inequality and causality.