THE EVOLUTION OF THE DIRAC FIELD IN CURVED SPACE-TIMES

Analogously to the recently published treatise 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 there is no particle creation by black holes, cf. [24, 16, 10, 15]. Moreover, the operator A = -ih(-1) D in expanding Robertson-Walker universes is shown to be dissipative, whereas in the contracting case -A is dissipative.