The Hawking Radiation as Gravitational Fowler-Nordheim Emission in Uniformly Accelerated Frame, in The Non-Relativistic Scenario

TL;DR

This paper proposes that Hawking radiation, traditionally viewed as quantum tunneling at a black hole horizon, can be interpreted as a Fowler-Nordheim field emission process in a non-relativistic, uniformly accelerated frame, linking quantum field theory and condensed matter phenomena.

Contribution

It introduces a novel non-relativistic interpretation of Hawking radiation as Fowler-Nordheim emission, connecting black hole physics with electron emission processes under acceleration.

Findings

Hawking radiation can be modeled as Fowler-Nordheim emission in non-relativistic frames.

The Schrödinger equation near the horizon matches that of electron emission under electrostatic fields.

The particle production mechanism aligns with Schwinger's process in quantum field theory.

Abstract

In the conventional scenario, the Hawking radiation is believed to be a tunneling process at the event horizon of the black hole. In the quantum field theoretic approach the Schwinger's mechanism is generally used to give an explanation of this tunneling process. It is the decay of quantum vacuum into particle anti-particle pairs near the black hole surface. However, in a reference frame undergoing an uniform accelerated motion in an otherwise flat Minkowski space-time geometry, in the non-relativistic approximation, the particle production near the event horizon of a black hole may be treated as a kind of Fowler-Nordheim field emission, which is the typical electron emission process from a metal surface under the action of an external electrostatic field. This type of emission from metal surface is allowed even at extremely low temperature. It has been noticed that in one-dimensional scenario, the Schr$\ddot{\rm{o}}$dinger equation satisfied by the created particle (anti-particle) near the event horizon, can be reduced to a differential form which is exactly identical with that obeyed by an electron immediately after the emission from the metal surface under the action of a strong electrostatic field. The mechanism of particle production near the event horizon of a black hole is therefore identified with Schwinger process in relativistic quantum field theory, whereas in the non-relativistic scenario it may be interpreted as Fowler-Nordheim emission process, when observed from an uniformly accelerated frame.