Price's law on nonstationary space-times

Jason Metcalfe, Daniel Tataru, Mihai Tohaneanu

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


In this article, we study the pointwise decay properties of solutions to the wave equation on a class of nonstationary 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 (Price's law, Price (1972)[54]) for linear waves. As a corollary, we also prove Price's law for certain small perturbations of the Kerr metric. This result was previously established by the second author in (Tataru [65]) on stationary backgrounds. The present work was motivated by the problem of nonlinear stability of the Kerr/Schwarzschild solutions for the vacuum Einstein equations, which seems to require a more robust approach to proving linear decay estimates.

Original languageEnglish
Pages (from-to)995-1028
Number of pages34
JournalAdvances in Mathematics
Issue number3
StatePublished - Jun 20 2012

Bibliographical note

Funding Information:
The first author was partially supported by NSF grant DMS0800678 . The second author was partially supported by NSF grant DMS0354539 and by the Miller Foundation .


  • Kerr
  • Nonstationary
  • Pointwise decay
  • Wave equation

ASJC Scopus subject areas

  • General Mathematics


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