Local decay of waves on asymptotically flat stationary space-times

By D. Tataru. 2009

208 citations recorded by the source corpus.

Author(s): Tataru, Daniel | Abstract: In this article we study the pointwise decay properties of solutions to the wave equation on a class of stationary 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 for linear waves. This work was motivated by open problems concerning decay rates for linear waves on Schwarzschild and Kerr backgrounds, where such a decay rate has been conjectured by R. Price. Our results apply to both of these cases.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3dcae2beaa131db7f3a7ebb71fd48c6ec9a3273c

How researchers see this paper

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

In Mathematical Physics

In Nuclear and High Energy Physics

Citations in the corpus

The global non-linear stability of the Kerr-de Sitter family of black holes (2016, methodology): “After pioneering work by Wald [Wal79] and Kay–Wald [KW87], Dafermos, Rodnianski and Shlapentokh-Rothman [DR10, DRSR14] recently proved polynomial decay for the scalar wave equation on all (exact) subextremal Kerr spacetimes; Tataru and Tohaneanu [Tat13, TT11] proved Price’s law, i.e. precise polynom”
Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M (2014, methodology): “To obtain from our Theorem alternative more refined corollaries for compactly supported smooth initial data, see [61].”
Hidden symmetries and decay for the wave equation on the Kerr spacetime (2009, background): “These include a pointwise decay estimate with rate t−1+ [20], a pointwise in time decay with rate t−3/2+ [36] (see also [18]), a Strichartz estimate [52], decay with rate t−3 [48].”
Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I (2011, methodology): “Two new methods were presented recently for obtaining sharp decay of energy flux and pointwise decay on black hole spacetimes; see [26, 50 ].”