Upper bound on the energies of the emitted Hawking quanta

TL;DR

This paper derives an upper bound on the energies of Hawking radiation emitted by Schwarzschild black holes using Thorne's hoop conjecture, showing that self-gravity effects prevent high-energy modes from escaping.

Contribution

It introduces a novel upper bound on Hawking quanta energies based on classical and quantum considerations, incorporating non-linear self-gravity effects.

Findings

Hawking quanta energies are bounded by ${ m extstyle rac{ ext{ extbar} ext{ extbar} ext{ extbar}}{ ext{ extbar} M^{1/3}}}$.

Higher energy modes are re-absorbed due to self-gravity effects.

The bound constrains the spectrum of emitted Hawking radiation.

Abstract

Using Thorne's hoop conjecture, it is argued that the energies of the Hawking quanta emitted from canonical Schwarzschild black holes are bounded from above by the simple quantum relation ${\cal E}<{\cal E}_{\text{max}}={\hbar^{2/3}}/M^{1/3}$. In particular, it is shown that, due to non-linear (self-gravity) effects of the tunneling quanta, higher energy field modes are re-absorbed (rather than escape to infinity) by the black hole.