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The evolution of the Dirac field in curved space-times. (English) Zbl 0865.58044

In this article the covariant Dirac equation of a spacetime in certain coordinate charts is rewritten as an evolution equation \(\frac{\partial\psi}{\partial t}=A\psi\). As a result it is proved that the Dirac operator \(D=ihA\) in the whole outer space of a Kerr-Newman black hole is symmetric. Furthermore it is shown that the operator \(A\) in expanding Robertson-Walker universe and the operator \(-A\) in the contracting case are dissipative.
Reviewer: H.Baum (Berlin)

MSC:

58J35 Heat and other parabolic equation methods for PDEs on manifolds
81T20 Quantum field theory on curved space or space-time backgrounds
53B50 Applications of local differential geometry to the sciences
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
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