  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.
