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 $S/E$.
Categories: hep-th