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arXiv · 1401.0465

Localized energy estimates on Myers-Perry space-times

Parul Laul·Jason Metcalfe·Shreyas Tikare·Mihai Tohaneanu
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Abstract

Localized energy estimates for the wave equation have been increasingly used to prove various other dispersive estimates. This article focuses on proving such localized energy estimates on $(1+4)$-dimensional Myers-Perry black hole backgrounds with small angular momenta. The Myers-Perry space-times are generalizations of higher dimensional Kerr backgrounds where additional planes of rotation are availabile while still maintaining axial symmetry. Once it is determined that all trapped geodesics have constant $r$, the method developed by Tataru and the fourth author, which perturbs off of the Schwarzschild case by using a pseudodifferential multiplier, can be adapted.

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Parul Laul, Jason Metcalfe, Shreyas Tikare, Mihai Tohaneanu. 2014-01-02. Localized energy estimates on Myers-Perry space-times. https://arxiv.org/abs/1401.0465

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