# 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]]