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Mode stability on the real axis

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arxiv 1607.02759 v2 pith:TTBMH7GP submitted 2016-07-10 gr-qc math.AP

classification gr-qcmath.AP
keywords equationpurelyteukolskyrealfrequencieshorizoninfinityingoing
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A generalization of the mode stability result of Whiting (1989) for the Teukolsky equation is proved for the case of real frequencies. The main result of the paper states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish. This has the consequence, that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation which are purely ingoing at the horizon, and purely outgoing at infinity, respectively. This fact yields a representation formula for solutions of the inhomogenous Teukolsky equation.

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  1. Teukolsky formalism for nonlinear Kerr perturbations

    gr-qc 2019-08 conditional novelty 8.0 of 10

    A new decomposition expresses sourced linearized perturbations of Kerr as a corrector tensor plus a Hertz potential, enabling an iterative scheme for nonlinear perturbations.

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