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  A note on the Klein–Gordon equation in the background of a rotating black hole

Beyer, H. R. (2009). A note on the Klein–Gordon equation in the background of a rotating black hole. Journal of Mathematical Physics, 50(1): 012502. doi:10.1063/1.3037327.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-3369-E Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-336B-A
Genre: Journal Article

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JoMP50-012502.pdf (Publisher version), 117KB
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 Creators:
Beyer, Horst R.1, Author
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1Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24013              

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 Abstract: 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.

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Language(s): eng - English
 Dates: 2009-01-06
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1063/1.3037327
eDoc: 337637
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Title: Journal of Mathematical Physics
Source Genre: Journal
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Publ. Info: Woodbury, N.Y. [etc.] : American Institute of Physics
Pages: - Volume / Issue: 50 (1) Sequence Number: 012502 Start / End Page: - Identifier: ISSN: 0022-2488