کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6425954 | 1345399 | 2012 | 34 صفحه PDF | دانلود رایگان |

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 tâ3 local uniform decay rate (Price's law, Price (1972)Â [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.
Journal: Advances in Mathematics - Volume 230, Issue 3, 20 June 2012, Pages 995-1028