A new physical-space approach to decay for the wave equation with applications to black hole spacetimes

Details A new physical-space approach to decay for the wave equation with applications to black hole spacetimes A new physical-space approach to decay for the wave equation with applications to black hole spacetimes

2009-10-26

arxiv.org/abs/0910.4957v1

XVIth International Congress on Mathematical Physics, P. Exner (ed.), World Scientific, London, 2009, pp. 421-433

Mathematics

Analysis of PDEs

14 pages, 2 figures, submitted to proceedings of the ICMP, Prague, August 2009

Scientific paper

We present a new general method for proving global decay of energy through a suitable spacetime foliation, as well as pointwise decay, starting from an integrated local energy decay estimate. The method is quite robust, requiring only physical space techniques, and circumvents use of multipliers or commutators with weights growing in t. In particular, the method applies to a wide class of perturbations of Minkowski space as well as to Schwarzschild and Kerr black hole exteriors.

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