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

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.

References in corpus (2)

• Decay of Solutions of the Wave Equation in the Kerr Geometry
• On a new symmetry of the solutions of the wave equation in the background of a Kerr black hole

Cited by in corpus (2)

• On the stability of the massive scalar field in Kerr space-time
• Wavy way to the Kerr metric and the quantum nature of its ring singularity