期刊
ANNALES HENRI POINCARE
卷 21, 期 4, 页码 1045-1111出版社
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00023-020-00900-w
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资金
- FCT/Portugal [UID/MAT/04459/2013, PTDC/MAT-ANA/1275/2014, SFRH/BPD/115959/2016]
We consider solutions of the massless scalar wave equation g. = 0, without symmetry, on fixed subextremal Kerr backgrounds (M, g). It follows from previous analyses in the Kerr exterior that for solutions. arising from sufficiently regular data on a two-ended Cauchy hypersurface, the solution and its derivatives decay suitably fast along the event horizon H+. Using the derived decay rate, we show that. is in fact uniformly bounded, |.| = C, in the black hole interior up to and including the bifurcate Cauchy horizon CH+, to which. in fact extends continuously. In analogy to our previous paper [31], on boundedness of solutions to the massless scalar wave equation on fixed subextremal Reissner-Nordstrom backgrounds, the analysis depends on weighted energy estimates, commutation by angular momentum operators and an application of Sobolev embedding. In contrast to the Reissner-Nordstrom case, the commutation leads to additional error terms that have to be controlled.
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