On subextremal Kerr backgrounds, solutions of the scalar wave equation arising from sufficiently regular localized data are uniformly bounded and extend continuously to the Cauchy horizon.
Quasi-Spherical Light Cones of the Kerr Geometry
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abstract
Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry that are asymptotic to Minkowski light cones at infinity. We develop the equations of these surfaces and examine their properties. In particular, we show that they are free of caustics for all positive values of the Kerr radial coordinate r. Useful applications include the propagation of high-frequency waves, the definition of Kruskal-like coordinates for a spinning black hole and the characteristic initial-value problem.
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Boundedness of massless scalar waves on Kerr interior backgrounds
On subextremal Kerr backgrounds, solutions of the scalar wave equation arising from sufficiently regular localized data are uniformly bounded and extend continuously to the Cauchy horizon.