Pointwise decay for the wave equation on nonstationary spacetimes

Abstract

The first article in a two-part series (the second article being [arXiv:2205.13197]) assumes a weak local energy decay estimate holds and proves that solutions to the linear wave equation with variable coefficients in ${\mathbb{R}}^{1+3}$, first-order terms, and a potential decay at a rate depending on how rapidly the vector fields of the metric, first-order terms, and potential decay at spatial infinity. We prove results for both stationary and nonstationary metrics. The proof uses local energy decay to prove an initial decay rate, and then uses the one-dimensional reduction repeatedly to achieve the full decay rate.

arXiv comment40 pages; some corrections; added a new remark and a new lemma

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Cited by in corpus (5)

• A sharp version of Price's law for wave decay on asymptotically flat spacetimes
• Pointwise decay for semilinear wave equations on Kerr spacetimes
• Integrated Local Energy Decay for Damped Magnetic Wave Equations on Stationary Space-Times
• Price's law on Minkowski space in the presence of an inverse square potential
• Sharp decay for Teukolsky equation in Kerr spacetimes