Bekenstein inequalities and nonlinear electrodynamics

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.

Entropy bounds and nonlinear electrodynamics

“…Starting from the fact that the entropy is always nonnegative, Dain [14] derived three subsidiary inequalities relating the size, charge, angular momentum, and energy as direct consequences of (2) and proved that they hold for any field configuration obeying Maxwell electrodynamics in flat spacetime. However, it can be shown [15] that nonlinear electrodynamics (NLED) easily violates the inequalities presented in [14]. Thus, one must recognize that Bekenstein's inequalities might be theorydependent.…”

Entropy bound in Einstein-Born-Infeld black holes

“…We shall analyze the entropy bound in the context of nonlinear electrodynamics (NLED). In particular, we consider the Born-Infeld (BI) electrodynamics [15][16][17] that, among NLED, has several interesting features: avoidance of classical singularity, it emerges as the lowenergy regime of string theory [18] and has no birefringence [19,20] (see also [21,22] and references therein). We shall repeat the same thought experiment proposed by Bekenstein and collaborators of slowly lowering a test body into the black hole but now generalizing for a charged body obeying BI electrodynamics in the curved spacetime of an Einstein-Born-Infeld black hole (EBI-BH).…”