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## Abstract

We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant t . We also prove the convergence of each solution to a stationary Coulomb solution. We separate a general solution into the charged, Coulomb part and the uncharged part. Convergence to the Coulomb solutions follows from the fact that the uncharged part satisfies a Morawetz estimate, i.e. that a spatially localised energy density is integrable in time. For the unchanged part, we study both the full Maxwell equation and the Fackerell-Ipser equation for one component. To treat the Fackerell-Ipser equation, we use a Fourier transform in t . For the Fackerell-Ipser equation, we prove a refined Morawetz estimate that controls 3/2 derivatives with no loss near the orbiting null geodesics.

Original language | English |
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Pages (from-to) | 689-743 |

Journal | Journal of Hyperbolic Differential Equations |

Volume | 12 |

Issue number | 4 |

DOIs | |

Publication status | Published - 31 Dec 2015 |

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## Projects

- 1 Finished