Journal
REVIEWS IN MATHEMATICAL PHYSICS
Volume 16, Issue 1, Pages 29-123Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129055X04001911
Keywords
Dirac equation; general relativity; Goursat problem; Kerr metric; scattering theory
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For the massless Dirac equation outside a slow Kerr black hole, we prove asymptotic completeness. We introduce a new Newman-Penrose tetrad in which the expression of the equation contains no artificial long-range perturbations. The main technique used is then a Mourre estimate. The geometry near the horizon requires us to apply a unitary transformation before we find ourselves in a situation where the generator of dilations is a good conjugate operator. The results are eventually re-interpreted geometrically to provide the solution to a Goursat problem on the Penrose compactified exterior.
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