Hawking tunneling and boomerang behaviour of massive particles with E < m

TL;DR

This paper investigates the tunneling behavior of massive particles with energy less than their mass in black hole radiation, revealing a boomerang trajectory and calculating detection probabilities near the horizon.

Contribution

It introduces a formalism to analyze E < m particle tunneling and demonstrates their boomerang-like classical trajectories in black hole and analogue gravity contexts.

Findings

E < m particles exhibit boomerang trajectories.

Detection probability depends on distance from the horizon.

Tunneling formalism applies to astrophysical and analogue black holes.

Abstract

Massive particles are radiated from black holes through the Hawking mechanism together with the more familiar radiation of massless particles. For $E >= m$, the emission rate is identical to the massless case. But $E < m$ particles can also tunnel across the horizon. A study of the dispersion relation and wave packet simulations show that their classical trajectory is similar to that of a boomerang. The tunneling formalism is used to calculate the probability for detecting such $E < m$ particles, for a Schwarzschild black hole of astrophysical size or in an analogue gravity experiment, as a function of the distance from the horizon and the energy of the particle.