On dispersion relations and the statistical mechanics of Hawking radiation

TL;DR

This paper investigates how different dispersion relations influence the statistical mechanics and emission spectrum of Hawking radiation, finding that large black holes exhibit a universal linear dispersion relation regardless of the statistical assumptions.

Contribution

It demonstrates that both canonical and microcanonical models predict a linear dispersion relation for large black holes and shows that modified high-momentum spectra do not significantly alter black hole luminosity.

Findings

Large black holes have a universal linear dispersion relation.

Modified spectra at high momenta do not significantly change luminosity.

Canonical and microcanonical models agree on dispersion relation for large black holes.

Abstract

We analyze the interplay between dispersion relations for the spectrum of Hawking quanta and the statistical mechanics of such a radiation. We first find the general relation between the occupation number density and the energy spectrum of Hawking quanta and then study several cases in details. We show that both the canonical and the microcanonical picture of the evaporation lead to the same linear dispersion relation for relatively large black holes. We also compute the occupation number obtained by instead assuming that the spectrum levels out (and eventually falls to zero) for very large momenta and show that the luminosity of black holes is not appreciably affected by the modified statistics.