Proof of the entropy bound on dynamical horizons

TL;DR

This paper proves the entropy bound conjecture for black hole dynamical horizons, demonstrating it follows from the generalized Bousso bound and unifying related entropy bounds, thus supporting the generalized second law.

Contribution

The paper provides a proof of the entropy bound on dynamical horizons and links it to the generalized Bousso bound, unifying lightlike and spacelike bounds.

Findings

Entropy bound on dynamical horizons is proved.

The bound follows from the generalized Bousso bound.

Lightlike and spacelike bounds are unified.

Abstract

The entropy bound conjecture concerning black hole dynamical horizons is proved. The conjecture states, if a dynamical horizon, $D_H$, is bounded by two surfaces with areas of $A_B$ and $\abp$ ($\abp>A_B$), then the entropy, $S_D$, that crosses $D_H$ must satisfy $S_D\leq {1/4}(\abp-A_B)$. We show that this conjecture is implied by the generalized Bousso bound. Consequently, the generalized second law holds for dynamical horizons. Finally, we show that the lightlike bousso bound and its spacelike counterpart can be unified as one bound.