Bekenstein Bound and Spectral Geometry

TL;DR

This paper explores how spectral geometry can be used to estimate the Bekenstein bound for various geometries, suggesting isospectral domains share the same entropy-energy ratio without requiring exact spectral data.

Contribution

It introduces a method to estimate the Bekenstein bound using spectral geometry relations, broadening the understanding of entropy-energy limits in different geometries.

Findings

Spectral relations can estimate the Bekenstein bound without exact spectra.

Isospectral domains share the same entropy-energy ratio.

Proposes a new approach to study entropy bounds in complex geometries.

Abstract

In this letter it is proposed to study the Bekenstein's $\xi(4)$ calculation of the $S/E$ bound for more general geometries. It is argued that, using some relations among eigenvalues obtained in the context of Spectral Geometry, it is possible to estimate $\xi(4)$ without an exact analytical knowledge of the spectrum. Finally it is claimed that isospectrality can define a class of domains with the same ratio $S/E$.