The holographic entropy bound in higher-dimensional spacetimes: As strong as ever

TL;DR

This paper proves that the holographic entropy bound remains valid for homogeneous thermal fields in higher-dimensional spacetimes, resolving previous apparent violations and confirming the bound's robustness in such scenarios.

Contribution

It demonstrates that homogeneity imposes an upper limit on entropy, ensuring the holographic bound holds even in higher-dimensional contexts where violations seemed possible.

Findings

Confirms the holographic entropy bound in higher dimensions.

Shows homogeneity constrains entropy, preventing violations.

Resolves previous theoretical challenges to the bound's universality.

Abstract

The celebrated holographic entropy bound asserts that, within the framework of a self-consistent quantum theory of gravity, the maximal entropy (information) content of a physical system is given by one quarter of its circumscribing area: $S\leq S_{\text{max}}={\cal A}/4{\ell^2_P}$ (here $\ell_P$ is the Planck length). An intriguing possible counter-example to this fundamental entropy bound, which involves {\it homogenous} weakly self-gravitating confined thermal fields in higher-dimensional spacetimes, has been proposed almost a decade ago. Interestingly, in the present paper we shall prove that this composed physical system, which at first sight seems to violate the holographic entropy bound, actually conforms to the entropy-area inequality $S\leq {\cal A}/4{\ell^2_P}$. In particular, we shall explicitly show that the homogeneity property of the confined thermal fields sets an upper bound on the entropy content of the system. The present analysis therefore resolves the apparent violation of the holographic entropy bound by confined thermal fields in higher-dimensional spacetimes.