Hawking radiation and the boomerang behaviour of massive modes near a horizon

TL;DR

This paper investigates the behavior of massive modes near black hole horizons, revealing a boomerang effect where certain modes are emitted, bounce back at a red horizon, and are re-absorbed, resolving a paradox in Hawking radiation models.

Contribution

It introduces a detailed analysis of massive mode dynamics near horizons, resolving a paradox between emission and absorption pictures of Hawking radiation.

Findings

Massive modes can be emitted and then re-absorbed by the black hole.

A red horizon causes bouncing of massive modes, affecting their propagation.

The results have implications for analogue gravity experiments.

Abstract

We discuss the behaviour of massive modes near a horizon based on a study of the dispersion relation and wave packet simulations of the Klein-Gordon equation. We point out an apparent paradox between two (in principle equivalent) pictures of black hole evaporation through Hawking radiation. In the picture in which the evaporation is due to the emission of positive-energy modes, one immediately obtains a threshold for the emission of massive particles. In the picture in which the evaporation is due to the absorption of negative-energy modes, such a threshold apparently does not exist. We resolve this paradox by tracing the evolution of the positive-energy massive modes with an energy below the threshold. These are seen to be emitted and move away from the black hole horizon, but they bounce back at a "red horizon" and are re-absorbed by the black hole, thus compensating exactly for the difference between the two pictures. For astrophysical black holes, the consequences are curious but do not affect the terrestrial constraints on observing Hawking radiation. For analogue gravity systems with massive modes, however, the consequences are crucial and rather surprising.