A Time Independent Energy Estimate for Outgoing Scalar Waves in the Kerr Geometry

Details A Time Independent Energy Estimate for Outgoing Scalar Waves in the Kerr Geometry A Time Independent Energy Estimate for Outgoing Scalar Waves in the Kerr Geometry

2007-07-16

arxiv.org/abs/0707.2290v2

J. Hyperbolic Differ. Equ.5:221-255, 2008

Physics

Mathematical Physics

31 pages, LaTeX, minor changes (published version)

Scientific paper

The Cauchy problem for the scalar wave equation in the Kerr geometry is considered, with initial data which is smooth and compactly supported outside the event horizon. A time-independent energy estimate for the outgoing wave is obtained. As an application we estimate the outgoing energy for wave-packet initial data, uniformly as the support of the initial data is shifted to infinity. The main mathematical tool is our previously derived integral representation of the wave propagator.

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