The evolution of the Dirac field in curved space-times

Analogously to the recently published treatise on the massless spin-s wave fields fors=1/2 ands=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 Diract operatorD 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 there is no particle creation by black holes, cf. [24, 16, 10, 15]. Moreover, the operatorA=−ih ⁻¹ D in expanding Robertson-Walker universes is shown to be dissipative, whereas in the contracting case −A is dissipative. This article was processed by the author using the LaT_EX style filecljour1 from Springer-Verlag