paper

Hidden symmetries and decay for the wave equation on the Kerr spacetime

arXiv:0908.2265

Abstract

Energy and decay estimates for the wave equation on the exterior region of slowly rotating Kerr spacetimes are proved. The method used is a generalization of the vector-field method, which allows the use of higher-order symmetry operators. In particular, our method makes use of the second-order Carter operator, which is a hidden symmetry in the sense that it does not correspond to a Killing symmetry of the spacetime.

50 pages, pdflatex. v3 proves the existence of a uniformly bounded energy and a Morawetz estimate. v1-2 also included a proof of a pointwise, almost-inverse-linear power-law decay estimate. The additional proof from v1-2, while correct, is a distraction from the generalised vector-field method and has been omitted from v3, which is to appear in http://annals.math.princeton.edu/articles/9459

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