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Linear Waves in the Interior of Extremal Black Holes II

Published version
Peer-reviewed

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Abstract

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, Communications in Mathematical Physics 353 (2017), no. 2, 717–770] for extremal Reissner-Nordström 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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Keywords

gr-qc, gr-qc, math.AP

Journal Title

Annales Henri Poincare

Conference Name

Journal ISSN

1424-0637
1424-0661

Volume Title

18

Publisher

Springer Nature
Sponsorship
EPSRC (1197314)
This work was supported by the European Research Council grant no. ERC-2011-StG 279363-HiDGR.