Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-05-28
Invent. Math. 185 (2011), 467-559
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
71 pages, 3 figures
Scientific paper
We consider Kerr spacetimes with parameters a and M such that |a|<< M, Kerr-Newman spacetimes with parameters |Q|<< M, |a|<< M, and more generally, stationary axisymmetric black hole exterior spacetimes which are sufficiently close to a Schwarzschild metric with parameter M>0, with appropriate geometric assumptions on the plane spanned by the Killing fields. We show uniform boundedness on the exterior for sufficiently regular solutions to the scalar homogeneous wave equation. In particular, the bound holds up to and including the event horizon. No unphysical restrictions are imposed on the behaviour of the solution near the bifurcation surface of the event horizon. The pointwise estimate derives in fact from the uniform boundedness of a positive definite energy flux. Note that in view of the very general assumptions, the separability properties of the wave equation on the Kerr background are not used.
Dafermos Mihalis
Rodnianski Igor
No associations
LandOfFree
A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-416332