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

Andersson, L., & Blue, P. (2015). Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior. Journal of Hyperbolic Differential Equations, 12(4), 689-743. doi:10.1142/S0219891615500204.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-007B-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-6308-B
Genre: Journal Article

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1310.2664.pdf (Preprint), 505KB
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 Creators:
Andersson, Lars1, Author              
Blue, Pieter, Author
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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Free keywords: Mathematics, Analysis of PDEs, math.AP,General Relativity and Quantum Cosmology, gr-qc,
 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.

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 Dates: 2013-10-092015-09-03201520152015
 Publication Status: Published in print
 Pages: 50 pages. v3 minor typographical changes
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 Identifiers: arXiv: 1310.2664
DOI: 10.1142/S0219891615500204
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Title: Journal of Hyperbolic Differential Equations
Source Genre: Journal
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Pages: - Volume / Issue: 12 (4) Sequence Number: - Start / End Page: 689 - 743 Identifier: -