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Local decay of waves on asymptotically flat stationary space-times
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 135, Number 2, April 2013
- pp. 361-401
- 10.1353/ajm.2013.0012
- Article
- Additional Information
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. Our results apply to both of these cases.