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 generalisation of the vector-field method that 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.

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Authors

Lars Andersson

Albert Einstein Institute, Max Planck Institute for Gravitational Physics, Potsdam, Germany Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

Pieter Blue

The School of Mathematics and the Maxwell Institute, University of Edinburgh, Edinburgh, Scotland, UK