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

L. Andersson, P. Blue

Research output: Working paper

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
PublisherArXiv
Publication statusPublished - 9 Oct 2013

Keywords

  • math.AP
  • gr-qc
  • 35Q75

Fingerprint

Dive into the research topics of 'Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior'. Together they form a unique fingerprint.

Cite this