Journal
ADVANCES IN MATHEMATICS
Volume 230, Issue 3, Pages 995-1028Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2012.03.010
Keywords
Wave equation; Kerr; Nonstationary; Pointwise decay
Categories
Funding
- NSF [DMS0800678, DMS0354539]
- Miller Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0800678, 0801261] Funding Source: National Science Foundation
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In this article, we study the pointwise decay properties of solutions to the wave equation on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time we establish a t(-3) local uniform decay rate (Price's law, Price (1972) [54]) for linear waves. As a corollary, we also prove Price's law for certain small perturbations of the Kerr metric. This result was previously established by the second author in (Tataru [65]) on stationary backgrounds. The present work was motivated by the problem of nonlinear stability of the Kerr/Schwarzschild solutions for the vacuum Einstein equations, which seems to require a more robust approach to proving linear decay estimates, (C) 2012 Elsevier Inc. All rights reserved.
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