language: en

arXiv:0802.3824v1 [gr-qc] 26 Feb 2008

A new result on the Klein-Gordon equation in the background of a rotating black hole

Horst R. Beyer
Louisiana State University (LSU) Center for Computation & Technology (CCT)
235 Johnston Hall LA 70803, USA
& Max Planck Institute for Gravitational Physics Albert Einstein Institute (AEI)
Am Mühlenberg 1 D-14476 Potsdam, Germany
February 26, 2008

Abstract This short paper should serve as 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 L 2 -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 L 2 -space and in this way generalizes a corresponding result of Kay (1985) in the case of the Schwarzschild black hole. It is believed that the employed methods are applicable to other separable wave equations.

1 General Introduction