Mathematical Research Letters

Volume 30 (2023)

Number 3

Generalized Price’s law on fractional-order asymptotically flat stationary spacetimes

Pages: 865 – 911

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n3.a10

Authors

Katrina Morgan (Department of Mathematics, Temple University, Philadelphia, Pennsylvania, U.S.A.)

Jared Wunsch (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)

Abstract

We obtain estimates on the rate of decay of a solution to the wave equation on a stationary spacetime that tends to Minkowski space at a rate $O ({\lvert x \rvert}^{-\kappa}), \kappa \in (1,\infty) \backslash \mathbb{N}$. Given suitably smooth and decaying initial data, we show a wave locally enjoys the decay rate $O(t^{-\kappa-2+\epsilon})$.

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The second author gratefully acknowledges support from Simons Foundation grant 631302. The first author gratefully acknowledges the support of NSF Postdoctoral Fellowship DMS-2002132.

Received 21 May 2021

Received revised 21 December 2021

Accepted 15 February 2022

Published 15 December 2023