Price's Law on Nonstationary Space-Times

By Jason Metcalfe, D. Tataru, Mihai Tohaneanu. 2011

138 citations recorded by the source corpus.

Abstract 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.

Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/61a91ed14124feadafb94e7d51044c188844c862

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Mathematical Physics

In Nuclear and High Energy Physics

Citations in the corpus

The linear stability of the Schwarzschild solution to gravitational perturbations (2016, background): “In the case of Schwarzschild, on the other hand, even for solutions arising from compactly supported initial data, though the decay rate (64) for φ can be indeed improved to t−3 [18, 28, 50], it cannot, for generic initial data, be further improved [45].”