# Bekenstein bound The Bekenstein bound says $S \leq 2 \pi E R / \hbar$, which is derived by requiring that dropping a box of matter with radius $R$ (when lowered say with a string to a point as close to the horizon as possible before dropping) into the BH does not make the total entropy lower. This equation does not involve $G$ and therefore is a non-gravitational statement. It was controversial when it was proposed although the [[0082 Generalised second law|generalised second law]] which gives rise to the Bekenstein bound was not controversial. ## Refs - original: - [[1981#Bekenstein]] - restricting to weaker conditions to avoid counterexmaples - [[2000#Bekenstein]] - [[0171 Covariant entropy bound|Bousso bound]] implies Bekenstein bound (a tight version) - shown in [[2002#Bousso (Oct)]] - Casini bound - [[2008#Casini]] - general understanding of quantum information aspects - [[2023#Hayden, Wang]] - covariant - [[2023#Kudler-Flam, Leutheusser, Rahman, Satishchandran, Speranza]]