Local decay of waves on asymptotically flat stationary space-times

Details Local decay of waves on asymptotically flat stationary space-times Local decay of waves on asymptotically flat stationary space-times

2009-10-28

arxiv.org/abs/0910.5290v2

Mathematics

Analysis of PDEs

33 pages; minor corrections, updated references

Scientific paper

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, where such a decay rate has been conjectured by R. Price. Our results apply to both of these cases.

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