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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Manuscripta Mathematica.
( Vol. 88 NO.2 / (1995))
The Evolution of the Dirac Field in Curved Space-Times
Andreas de Vries,
Pages. 233-246
Abstract Analogously to the recently published treatisc on the massless
spin-$s$ wave fields for $s=1/2$ and $s=1$, cf. [ 32 ], the
covariant Dirac equation in certain coordinate charts is
rewritten as an evolution equation. As a result it is proved that
the Dirac operator $D$ in the whole outer space of a Kerr-Newman
black hole is symmetric. This is different from the behavior of
the Maxwell operator which admits superradiance in case of a
rotating black hole, cf.[ 32 ]. An interpretation of this
symmetry may be that three is no particle creation by black
holes, cf.[ 24,16,10,15 ]. Moreover, the operator $A=-ihbar^{-1}D$
in expanding Robertson-Walker universes is shown to be
dissipative, whereas in the contracting case $-A$ is dissipative.
Contents 1. Introduction
2. Preliminaries
3. The Dirac operator
4. Bounds for Re$\langle \psi,A \psi \rangle$
5. Applications
5.1. The Kerr-Newman space-time
5.2. The Robertson-Walker universes
6. Discussion
A. The spin coefficients for the Robertson-Walker universes
Key words
Mathmatical Subject Classification