**Memoires de la Societe Mathematique de France**

Volume: 117;
2010;
158 pp;
Softcover

MSC: Primary 35; 58; 83;
**Print ISBN: 978-2-85629-284-6
Product Code: SMFMEM/117**

List Price: $42.00

Individual Member Price: $33.60

# Creation of Fermions by Rotating Charged Black Holes

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*Dietrich Häfner*

A publication of the Société Mathématique de France

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.

#### Readership

Graduate students and research mathematicians interested in differential equations.