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Linear waves in the interior of extremal black holes II
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We consider solutions to the linear wave equation in the interior region of extremal Kerr black holes. We show that axisymmetric solutions can be extended continuously beyond the Cauchy horizon and moreover that, if we assume suitably fast polynomial decay in time along the event horizon, their local energy is finite. We also extend these results to non-axisymmetric solutions on slowly rotating extremal Kerr-Newman black holes. These results are the analogues of results obtained in [D. Gajic, Linear waves in the interior of extremal black holes I, arXiv:1509.06568] for extremal Reissner-Nordstr\"om and stand in stark contrast to previously established results for the subextremal case, where the local energy was shown to generically blow up at the Cauchy horizon.
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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.
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