Light-sheets and Bekenstein's bound

TL;DR

From the covariant bound on the entropy of partial light sheets, a version of Bekenstein's bound is derived, where S, M, and x are the entropy, total mass, and width of any isolated, weakly gravitating system.

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.

Figures (1)

• Figure 1: Matter system $W$, light-sheet $L$, entry surface $\tilde{B}_+$, and exit surface $\tilde{B}_-$. At first order in $\delta g$, the bending of light leads to a small area difference between entry and exit surfaces, which bounds the entropy of $W$.