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Creation of Fermions by Rotating Charged Black Holes
Dietrich Häfner, Université Bordeaux 1, Talence, France
A publication of the Société Mathématique de France.
Mémoires de la Société Mathématique de France
158 pp; softcover
Number: 117
ISBN-10: 2-85629-284-4
ISBN-13: 978-2-85629-284-6
List Price: US$42
Member Price: US$33.60
Order Code: SMFMEM/117
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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. The author shows 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.

The author first introduces a model of the collapse of the star. He supposes 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.

The author formulates and proves 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 the author constructs explicitly a Penrose compactification of block \(I\) of the Kerr-Newman space-time based on simple null geodesics.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in differential equations.

Table of Contents

  • Introduction
  • Strategy of the proof and organization of the article
  • The model of the collapsing star
  • Classical Dirac fields
  • Dirac quantum fields
  • Additional scattering results
  • The characteristic Cauchy problem
  • Reductions
  • Comparison of the dynamics
  • Propagation of singularities
  • Proof of the main theorem
  • Bibliography
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