Proves threshold-sharp stability for the conformal scalar-curvature sector on Carter slabs and extends the framework to black hole exteriors like Kerr and Reissner-Nordström.
Decay of Solutions of the Wave Equation in the Kerr Geometry
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abstract
We consider the Cauchy problem for the scalar wave equation in the Kerr geometry for smooth initial data supported outside the event horizon. We prove that the solutions decay in time in L^\infty_loc. The proof is based on a representation of the solution as an infinite sum over the angular momentum modes, each of which is an integral of the energy variable on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation of variables.
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2026 1verdicts
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Threshold-Sharp Conformal Scalar Stability on Carter Slabs and Black Hole Exteriors
Proves threshold-sharp stability for the conformal scalar-curvature sector on Carter slabs and extends the framework to black hole exteriors like Kerr and Reissner-Nordström.