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

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