Hawking radiation of E<m massive particles in the tunneling formalism

TL;DR

This paper investigates Hawking radiation of massive particles using tunneling formalism, revealing that particles with energy less than their mass can tunnel across the horizon, extending the traditional understanding of black hole radiation.

Contribution

It introduces a method to calculate Hawking radiation for E<m particles and derives a general tunneling probability formula applicable near the horizon and at large distances.

Findings

Particles with E<m can tunnel across the horizon.

The tunneling probability depends on the particle's energy and distance from the horizon.

The formalism recovers traditional results for E>=m.

Abstract

We use the tunneling formalism to calculate the Hawking radiation of massive particles. For E>=m, we recover the traditional result, identical to the massless case. But E<m particles can also tunnel across the horizon in a Hawking process. We study the probability for detecting such E<m particles as a function of the distance from the horizon and the energy of the particle in the tunneling formalism. We derive a general formula and obtain simple approximations in the near-horizon limit and in the limit of large radii.