Journal
ANALYSIS & PDE
Volume 5, Issue 3, Pages 553-625Publisher
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/apde.2012.5.553
Keywords
Kerr spacetime; wave equation; decay estimates
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We prove that sufficiently regular solutions to the wave equation square(gK) Phi = 0 on the exterior of a sufficiently slowly rotating Kerr black hole obey the estimates vertical bar Phi vertical bar <= C(t(*))(-3/2+eta) on a compact region of r. This is proved with the help of a new vector field commutator that is analogous to the scaling vector field on Minkowski and Schwarzschild spacetime. This result improves the known robust decay rates that are proved using the vector field method in the region of finite r and along the event horizon.
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