Shedding new light on the absence of fermionic superradiance and maximal infalling rate of fermions into a black hole

TL;DR

This paper clarifies why fermionic superradiance does not increase black hole flux and identifies a maximum fermion infall rate linked to Hawking temperature, using a complete basis classification in rotating black hole backgrounds.

Contribution

It provides a detailed classification of bases in rotating black holes to distinguish superradiance from Hawking radiation and explains the absence of fermionic superradiance enhancement.

Findings

Fermions exhibit spontaneous particle creation outside the horizon for certain frequencies.

Superradiance does not increase the total flux due to Pauli exclusion.

A maximum fermion infall rate exists, governed by Hawking temperature.

Abstract

Using the complete classification of the bases in the rotating black hole background we separate superradiance from the Hawking effect. We first find that there is spontaneous particle creation for fermions by the potential outside the black hole horizon for the frequencies inside the superradiant regime, i.e. $\omega<k\Omega_H$. However, these particles do not enhance the total flux from the black hole. For the superradiance particle to became real, its negative energy counterpart has to be canceled by the positive energy Hawking radiation mode at the horizon. Since due to the Pauli's principle this cancellation must be one-to-one, the superradiance effect cannot add anything to the total black hole flux. For an extremal black hole, the Hawking temperature is zero, horizon is not populated with thermal modes, and fermions can be emitted through the superradiance mechanism. On the other hand, a macroscopic flux of fermions infalling to the black hole is the opposite process of Hawking radiation. A positive energy-infalling particle must cancel out a negative energy thermal mode at the horizon, which leaves a net positive energy mode that crosses the horizon. Since there is finite thermal particle density at the horizon, this implies that there is a maximal fermion infalling rate which is also controlled by the Hawking temperature.