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

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. © 2009 American Institute of Physics. DOI: 10.1063/1.3037327