Hawking radiation of massive modes and undulations

TL;DR

This paper analyzes how a small mass term affects Hawking radiation in analogue black hole systems, showing it leads to mode reflection, cancels infrared divergence, and saturates undulation amplitude, with new undulations in black hole flows.

Contribution

It introduces the effects of a small mass on Hawking radiation and undulations, revealing mode reflection, spectrum regularization, and new undulation phenomena.

Findings

Mass induces total reflection at low frequencies.

Infrared divergence in the spectrum is canceled by mode mixing.

Undulation amplitude saturates in white hole flows due to mass effects.

Abstract

We compute the analogue Hawking radiation for modes which posses a small wave vector perpendicular to the horizon. For low frequencies, the resulting mass term induces a total reflection. This generates an extra mode mixing that occurs in the supersonic region, which cancels out the infrared divergence of the near horizon spectrum. As a result, the amplitude of the undulation (0-frequency wave with macroscopic amplitude) emitted in white hole flows now saturates at the linear level, unlike what was recently found in the massless case. In addition, we point out that the mass introduces a new type of undulation which is produced in black hole flows, and which is well described in the hydrodynamical regime.