  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.
