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Price's law on nonstationary spacetimes

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If you have a question about this talk, please contact Jonathan Ben-Artzi.

This is a report on a joint work with D. Tataru and M. Tohaneanu. Here we look at pointwise decay of solutions to wave equations on certain asympototically flat spacetimes. Assuming a class of localized energy estimates, we show that a $t^{-3}$ uniform local decay rate holds. This corresponds to Price’s law. The class of localized energy estimates which are assumed are known to hold on the Schwarzschild spacetime and Kerr spacetimes with small angular momentums. Such decay rates were previously shown by Tataru on these stationary space-times. Our methods are more robust as, e.g., we additionally show that the localized energy estimates, and thus Price’s law, hold for certain classes of time-dependent perturbations of these spaces.

This talk is part of the Partial Differential Equations seminar series.

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