Kermions: quantization of fermions on Kerr space-time

TL;DR

This paper investigates quantum fermion fields in Kerr black hole spacetime, defining novel quantum states with attractive regularity properties, and compares them to bosonic states, revealing greater state-defining flexibility for fermions.

Contribution

It introduces new fermionic quantum states on Kerr spacetime, including a Boulware-like and Hartle-Hawking-like state, which have no bosonic analogues and exhibit desirable physical properties.

Findings

Defined fermionic Boulware-like and Hartle-Hawking-like states.

Numerically computed expectation values of fermion current and stress-energy tensor.

Identified regularity and physical properties of the new states.

Abstract

We study a quantum fermion field on a background non-extremal Kerr black hole. We discuss the definition of the standard black hole quantum states (Boulware, Unruh and Hartle-Hawking), focussing particularly on the differences between fermionic and bosonic quantum field theory. Since all fermion modes (both particle and anti-particle) have positive norm, there is much greater flexibility in how quantum states are defined compared with the bosonic case. In particular, we are able to define a candidate `Boulware'-like state, empty at both past and future null infinity; and a candidate `Hartle-Hawking'-like equilibrium state, representing a thermal bath of fermions surrounding the black hole. Neither of these states have analogues for bosons on a non-extremal Kerr black hole and both have physically attractive regularity properties. We also define a number of other quantum states, numerically compute differences in expectation values of the fermion current and stress-energy tensor between two states, and discuss their physical properties.