### Abstract

For any sub-extremal Kerr spacetime with non-zero angular momentum, we find an open family of non-zero masses for which there exist smooth, finite energy, and exponentially growing solutions to the corresponding Klein-Gordon equation. If desired, for any non-zero integer m, an exponentially growing solution can be found with mass arbitrarily close to (Formula presented). In addition to its direct relevance for the stability of Kerr as a solution to the Einstein-Klein-Gordon system, our result provides the first rigorous construction of a superradiant instability. Finally, we note that this linear instability for the Klein-Gordon equation contrasts strongly with recent work establishing linear stability for the wave equation.

Original language | English (US) |
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Pages (from-to) | 859-891 |

Number of pages | 33 |

Journal | Communications In Mathematical Physics |

Volume | 329 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2014 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics