Entropy bounds and nonlinear electrodynamics

Abstract

Bekenstein's inequality sets a bound on the entropy of a charged macroscopic body. Such a bound is understood as a universal relation between physical quantities and fundamental constants of nature that should be valid for any physical system. We reanalyze the steps that lead to this entropy bound considering a charged object in conformity to Born-Infeld electrodynamics and show that the bound depends of the underlying theory used to describe the physical system. Our result shows that the nonlinear contribution to the electrostatic self-energy causes a raise in the entropy bound. As an intermediate step to obtain this result, we exhibit a general way to calculate the form of the electric field for a given nonlinear electrodynamics in Schwarzschild spacetime.

Entropy bound in Einstein-Born-Infeld black holes

“…Notwithstanding, in a recent paper [22], it has been shown that the displacement vector of an arbitrary NLED in Schwarzschild spacetime is curl-free. In addition, assuming that the constitutive relations are invertible, the electrostatic potential solution can be written in terms of Linet's solution.…”

“…But in practice, one obtains only a numerical φ(x) since the above equation has no analytical solution. In [22], we have shown that a good approximation is to split the electric field as a sum of two terms…”

“…The ψ p (x) represents the added term to correct the asymptotic behavior of Copson's solution. As discussed in [22], ψ p (x) encodes the black hole horizon polarization due to the presence of the test charged particle. Alternatively, one can interpret this extra term as an image charge inside the black hole.…”

“…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).…”

Self-energy problem, vacuum polarization, and dual symmetry in Born-Infeld-type $U(1)$ gauge theories

“…On the other hand, the dynamics of electromagnetic fields on the world-volumes of D-branes are governed by BI theory. Since both the Einstein-Hilbert action (in an antide Sitter background) and BI effective action appear at low-energy limit of string theory models, coupling nonlinear electrodynamics to gravity has been found various applications in the literature, especially in the contexts of effective field theories, gauge/gravity duality and black hole physics [8,10,11,22,[38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56].…”