The evolution of the Dirac field in curved space-times

Andreas de Vries, published in: manuscripta mathematica 88, 27-45 (1995)

Based on a new approach to introduce evolution and linear functional analysis into general relativity, this article considers the Dirac equation in a general gravitational field as an evolution equation. As a result the Dirac operator D in the whole outer space of a charged rotating black hole ("Kerr-Newman space-time") is symmetric, different to the electromagnetic field operator. Thus there is no particle creation by black holes.

Moreover, the operator A = - i D in expanding Robertson-Walker universes is dissipative, whereas in the contracting case -A is dissipative.