Hawking radiation in dispersive theories, the two regimes

TL;DR

This paper analyzes how high-frequency dispersion affects Hawking radiation spectra, revealing two distinct regimes and providing insights relevant for analogue experiments and quantum gravity theories with Lorentz violation.

Contribution

It identifies two regimes of Hawking radiation spectrum in dispersive theories and characterizes the transition governed by a single parameter, extending understanding of quantum gravity and analogue models.

Findings

Spectrum diverges as inverse of Killing frequency

Two regimes: adiabatic and dispersion-regulated abrupt transition

Results applicable to analogue experiments and Lorentz-violating quantum gravity theories

Abstract

We compute the black hole radiation spectrum in the presence of high-frequency dispersion in a large set of situations. In all cases, the spectrum diverges like the inverse of the Killing frequency. When studying the low-frequency spectrum, we find only two regimes: an adiabatic one where the corrections with respect to the standard temperature are small, and an abrupt one regulated by dispersion, in which the near-horizon metric can be replaced by step functions. The transition from one regime to the other is governed by a single parameter which also governs the net redshift undergone by dispersive modes. These results can be used to characterize the quasiparticles spectrum of recent and future experiments aiming to detect the analogue Hawking radiation. They also apply to theories of quantum gravity which violate Lorentz invariance.