Vol. 5, No. 3, 2012

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A vector field method approach to improved decay for solutions to the wave equation on a slowly rotating Kerr black hole

Jonathan Luk

Vol. 5 (2012), No. 3, 553–625

We prove that sufficiently regular solutions to the wave equation gKΦ = 0 on the exterior of a sufficiently slowly rotating Kerr black hole obey the estimates |Φ| C(t)32+η 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.

Kerr spacetime, wave equation, decay estimates
Mathematical Subject Classification 2010
Primary: 83C99, 35R01
Received: 5 October 2010
Revised: 25 March 2011
Accepted: 21 April 2011
Published: 15 October 2012
Jonathan Luk
Department of Mathematics
Princeteon University
Fine Hall
Washington Road
Princeton, NJ 08544
United States