Bekenstein bounds in de Sitter and flat space

TL;DR

The paper connects the de Sitter D-bound for matter entropy to the flat-space Bekenstein bound, showing that in the dilute limit the D-bound reduces to the Bekenstein form when expressed through the gravitational radius and cosmological horizon. It extends both bounds to higher dimensions via a Geroch process and analyzes how the two bounds relate to the holographic bound, finding that black holes saturate the Bekenstein bound only in four dimensions and do not saturate the D-bound in higher dimensions. The work highlights a dimensional tension between entropy bounds and suggests possible interpolations or stronger foundational bounds, reinforcing the nuanced landscape of holographic ideas beyond flat space. Overall, it clarifies how Bekenstein-type limits extend to de Sitter and higher-dimensional spacetimes and where they cease to be tight or equivalent to holographic principles.

Abstract

The D-bound on the entropy of matter systems in de Sitter space is shown to be closely related to the Bekenstein bound, which applies in a flat background. This holds in arbitrary dimensions if the Bekenstein bound is calibrated by a classical Geroch process. We discuss the relation of these bounds to the more general bound on the entropy to area ratio. We find that black holes do not saturate the Bekenstein bound in dimensions greater than four.