Holographic entropy bound from gravitational Fock space truncation

TL;DR

This paper derives a holographic entropy bound from gravitationally constrained Fock space truncation in higher-dimensional asymptotically flat spacetimes, using scalar and fermionic fields confined in a spherical volume.

Contribution

It provides a simplified derivation of Yurtsever's holographic entropy bound result for both bosonic and fermionic fields in arbitrary dimensions.

Findings

Entropy bound scales with surface area of the volume

Bound is consistent with holographic principles

Method applies to both bosonic and fermionic fields

Abstract

A simplified derivation of Yurtsever's result, which states that the entropy of a truncated bosonic Fock space is given by a holographic bound when the energy of the Fock states is constrained gravitationally, is given for asymptotically flat spacetimes with arbitrary dimension d greater or equal to four. For this purpose, a scalar field confined to a spherical volume in d-dimensional spacetime is considered. Imposing an upper bound on the total energy of the corresponding Fock states which ensures that the system is in a stable configuration against gravitational collapse and imposing a cutoff on the maximum energy of the field modes of the order of the Planck energy leads to an entropy bound of holographic type. A simple derivation of the entropy bound is also given for the fermionic case.