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ID: 337637.0, MPI für Gravitationsphysik / Astrophysical Relativity
A note on the Klein–Gordon equation in the background of a rotating black hole
Authors:Beyer, Horst R.
Date of Publication (YYYY-MM-DD):2009-01-06
Title of Journal:Journal of Mathematical Physics
Volume:50
Issue / Number:1
Sequence Number of Article:012502
Review Status:not specified
Audience:Not Specified
Abstract / Description:This short paper should serve as a basis for further analysis of a previously found new symmetry of the solutions of the wave equation in the gravitational field of a Kerr black hole. Its main new result is the proof of essential self-adjointness of the spatial part of a reduced normalized wave operator of the Kerr metric in a weighted L2-space. As a consequence, it leads to a purely operator theoretic proof of the well posedness of the initial value problem of the reduced Klein–Gordon equation in that field in that L2-space and in this way generalizes a corresponding result of Kay [“The double-wedge algebra for quantum fields on Schwarzschild and Minkowski spacetimes,” Commun. Math. Phys. 100, 57 (1985)] in the case of the Schwarzschild black hole. It is believed that the employed methods are applicable to other separable wave equations.
External Publication Status:published
Document Type:Article
Communicated by:Bernhard F. Schutz
Affiliations:MPI für Gravitationsphysik/Astrophysical Relativity
Identifiers:LOCALID:arXiv:0802.3824
ISSN:1089-7658
DOI:10.1063/1.3037327
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