Fermions in Black Hole Space-Time: Hawking Radiation and Back Reaction

TL;DR

This paper investigates how fermionic matter fields influence the geometry of a Schwarzschild black hole, revealing that backreaction shifts the event horizon and alters Hawking radiation, with implications for quantum algebraic structures.

Contribution

It demonstrates the leading order metric correction due to fermionic backreaction, showing horizon shift and nontrivial fermionic exchange algebra in semiclassical gravity.

Findings

Horizon shift caused by fermionic backreaction.

Fermionic operators obey a nontrivial exchange algebra.

Hawking radiation is affected by the backreaction effects.

Abstract

The leading order correction to the metric of a Schwarzschild black hole, due to the backreaction of infalling fermionic matter fields, is shown to produce a shift of the event horizon such that particles that would constitute Hawking radiation at late retarded times are now trapped. Fermionic field operators associated with infalling and outgoing modes at the horizon behave canonically in the semiclassical approximation. They are, however, shown to satisfy a nontrivial exchange algebra given in terms of the backreaction, when the shift is `quantized' by means of correspondence. The consequent exchange algebra for bilinear fermionic densities is also obtained.