Local Decay of Waves on Asymptotically Flat Stationary Space-times
نویسنده
چکیده
In this article we study the pointwise decay properties of solutions to the wave equation on a class of stationary 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 for linear waves. This work was motivated by open problems concerning decay rates for linear waves on Schwarzschild and Kerr backgrounds. In the Schwarzschild case, such a decay rate has been heuristically derived by Price [39]. Our results apply to both of these cases.
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Price's Law on Nonstationary Space-Times
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 local uniform decay rate (Price’s law [54]) for linear waves. As a corollary, we also prove Pric...
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