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

Beyer, Horst R.

doi:10.1063/1.3037327

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

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Beyer, Horst R.
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-3369-E

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.