Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior

Lars Andersson, Pieter Blue

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)689-743
JournalJournal of Hyperbolic Differential Equations
Volume12
Issue number4
DOIs
Publication statusPublished - 31 Dec 2015

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