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On the stability of the massive scalar field in Kerr space-time

Beyer, H. R. (2011). On the stability of the massive scalar field in Kerr space-time. Journal of Mathematical Physics, 52(10): 102502. doi:10.1063/1.3653840.

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1105.4956 (Preprint), 246KB
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Creators:
Beyer, Horst Reinhard1, Author
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24012

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Free keywords: Mathematical Physics, math-ph,General Relativity and Quantum Cosmology, gr-qc,Mathematics, Analysis of PDEs, math.AP,Mathematics, Mathematical Physics, math.MP,
Abstract: The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon equation, describing the propagation of a scalar field in the background of a rotating (Kerr-) black hole. Results suggest that the stability of the field depends crucially on its mass $\mu$. Among others, the paper provides an improved bound for $\mu$ above which the solutions of the reduced, by separation in the azimuth angle in Boyer-Lindquist coordinates, Klein-Gordon equation are stable. Finally, it gives new formulations of the reduced equation, in particular, in form of a time-dependent wave equation that is governed by a family of unitarily equivalent positive self-adjoint operators. The latter formulation might turn out useful for further investigation. On the other hand, it is proved that from the abstract properties of this family alone it cannot be concluded that the corresponding solutions are stable.

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Dates: 2011-05-252011
Publication Status: Published in print
Pages: 30 pages, 2 figures
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1105.4956
DOI: 10.1063/1.3653840
Degree: -

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### Source 1

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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: 52 (10) Sequence Number: 102502 Start / End Page: - Identifier: ISSN: 0022-2488
CoNE: /journals/resource/954922836227