Creation of fermions by rotating charged black-holes

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.

139 pages, to appear in Mémoires de la SMF

References in corpus (2)

• On smooth Cauchy hypersurfaces and Geroch's splitting theorem
• An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

Cited by in corpus (8)

• Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes
• Linear Waves in the Kerr Geometry: A Mathematical Voyage to Black Hole Physics
• Asymptotic completeness for superradiant Klein-Gordon equations and applications to the De Sitter Kerr metric
• Recovering the mass and the charge of a Reissner-Nordström black hole by an inverse scattering experiment
• Integral Formula for the Characteristic Cauchy Problem on a curved Background
• Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
• Scattering theory for Dirac fields inside a Reissner-Nordström-type black hole
• Scattering theory for the Dirac equation on the Schwarzschild-Anti-de Sitter spacetime