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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

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. 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