Creation of fermions by rotating charged black-holes

TL;DR

This paper mathematically demonstrates that an observer far from a rotating charged black hole detects a thermal Hawking radiation effect for fermions during star collapse, using a detailed Kerr-Newman spacetime model.

Contribution

It provides a rigorous proof of the Hawking effect for fermions in a collapsing Kerr-Newman black hole setting, including new estimates and solution existence results.

Findings

Observer detects thermal state at infinity

Proves Hawking effect for fermions in Kerr-Newman spacetime

Develops new velocity estimates for Dirac fields

Abstract

This work is devoted to the mathematical study of the Hawking effect for fermions in the setting of the collapse of a rotating charged star. We show that an observer who is located far away from the star and at rest with respect to the Boyer Lindquist coordinates observes the emergence of a thermal state when his proper time goes to infinity. We first introduce a model of the collapse of the star. We suppose that the space-time outside the star is given by the Kerr-Newman metric. The assumptions on the asymptotic behavior of the surface of the star are inspired by the asymptotic behavior of certain timelike geodesics in the Kerr-Newman metric. The Dirac equation is then written using coordinates and a Newman-Penrose tetrad which are adapted to the collapse. This coordinate system and tetrad are based on the so called simple null geodesics. The quantization of Dirac fields in a globally hyperbolic space-time is described. We formulate and prove a theorem about the Hawking effect in this setting. The proof of the theorem contains a minimal velocity estimate for Dirac fields that is slightly stronger than the usual ones and an existence and uniqueness result for solutions of a characteristic Cauchy problem for Dirac fields in the Kerr-Newman space-time. In an appendix we construct explicitly a Penrose compactification of block I of the Kerr-Newman space-time based on simple null geodesics.