Decay and Non-Decay of the Local Energy for the Wave Equation on the De Sitter–Schwarzschild Metric

By Jean-François Bony, Dietrich Häfner. 2007

144 citations recorded by the source corpus.

We describe an expansion of the solution of the wave equation on the De Sitter–Schwarzschild metric in terms of resonances. The principal term in the expansion is due to a resonance at 0. The error term decays polynomially if we permit a logarithmic derivative loss in the angular directions and exponentially if we permit an $${\varepsilon}$$ derivative loss in the angular directions.

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

View Paper: https://www.semanticscholar.org/paper/941ce38e081b2cab3c4806bbda9757aa0256f406

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

Quasi-Normal Modes and Exponential Energy Decay for the Kerr-de Sitter Black Hole (2010, methodology): “This was further developed by Bony and Häfner in [11], who established an expansion of the solutions of the wave equation in terms of resonant states.”
Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov) (2010, methodology): “In special geometries (without the ability to add perturbations) such decay has been described by delicate separation of variables techniques, again see Bony-Häfner [5] in the De Sitter-Schwarzschild and Schwarzschild settings, but only away from the event horizons, and by Dyatlov [20, 19] in the K”
The evolution problem in general relativity (2008, methodology): “40 The relevant estimates on the distribution of these necessary for the analysis of [21] had been obtained earlier by Sá Barreto and Zworski [127].”
The global non-linear stability of the Kerr-de Sitter family of black holes (2016, background): “Previously, on Schwarzschild–de Sitter space, Bachelot [Bac91] set up the functional analytic scattering theory, and Sá Barreto–Zworski [SBZ97] and Bony–Häfner [BH08] studied resonances and decay away from the event horizon; Melrose, Sá Barreto and Vasy [MSBV14b] proved exponential decay to const”