Light-sheets and Bekenstein's bound

TL;DR

This paper derives a new version of Bekenstein's entropy bound from light-sheet principles, revealing a fundamental link between information, geometry, and gravity that generalizes previous bounds.

Contribution

It introduces a covariant derivation of Bekenstein's bound using light-sheets, unifying older entropy bounds under a more general framework.

Findings

Derived a tight entropy bound for weakly gravitating systems.

Connected light-sheet entropy bounds to black hole thermodynamics.

Showed the bound's applicability in various spatial directions.

Abstract

From the covariant bound on the entropy of partial light-sheets, we derive a version of Bekenstein's bound: S/M \leq pi x/hbar, where S, M, and x are the entropy, total mass, and width of any isolated, weakly gravitating system. Because x can be measured along any spatial direction, the bound becomes unexpectedly tight in thin systems. Our result completes the identification of older entropy bounds as special cases of the covariant bound. Thus, light-sheets exhibit a connection between information and geometry far more general, but in no respect weaker, than that initially revealed by black hole thermodynamics.