### Abstract

Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein equations-a major open question in the subject. Nonetheless, it is only very recently that even the most basic boundedness and quantitative decay properties of linear waves have been proven in a suitably general class of black hole exterior spacetimes. This talk will review our current mathematical understanding of waves on black hole backgrounds, beginning with the classical boundedness theorem of Kay and Wald on exactly Schwarzschild exteriors and ending with very recent boundedness and decay theorems (proven in collaboration with Igor Rodnianski) on a wider class of spacetimes. This class of spacetimes includes in particular slowly rotating Kerr spacetimes, but in the case of the boundedness theorem is in fact much larger, encompassing general axisymmetric stationary spacetimes whose geometry is sufficiently close to Schwarzschild and whose Killing fields span the null generator of the horizon.

Original language | English (US) |
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Title of host publication | Space Plasma Physics - School and Workshop on Space Plasma Physics |

Pages | 19-38 |

Number of pages | 20 |

DOIs | |

State | Published - 2009 |

Externally published | Yes |

Event | Spanish Relativity Meeting 2008 - Salamanca, Spain Duration: Sep 15 2008 → Sep 19 2008 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 1122 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Other

Other | Spanish Relativity Meeting 2008 |
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Country | Spain |

City | Salamanca |

Period | 9/15/08 → 9/19/08 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Keywords

- Black holes
- Kerr metric
- Wave equation

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## Cite this

*Space Plasma Physics - School and Workshop on Space Plasma Physics*(pp. 19-38). (AIP Conference Proceedings; Vol. 1122). https://doi.org/10.1063/1.3141255