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This paper establishes that on the domain of outer communications of a general class of stationary and asymptotically flat Lorentzian manifolds of dimension $d+1$, $d\ge3$, the local energy of solutions to the scalar wave equation $\square_{g}\psi=0$ decays at least with an inverse logarithmic rate.
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Classical and quantum scattering theory for linear scalar fields on the Schwarzschild metric I
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A proof of Price’s law for the collapse of a self-gravitating scalar field
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Uniform decay of local energy and the semi-linear wave equation on Schwarzschild space
P. Blue and J. Sterbenz · 2006
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A. Pomeransky and R. Sen’kov · 2006
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A note on energy currents and decay for the wave equation on a Schwarzschild background
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Effective limiting absorption principles, and applications
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A local energy estimate on Kerr black hole backgrounds
D. Tataru and M. Tohaneanu · 2011
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Decay of axisymmetric solutions of the wave equation on extreme Kerr backgrounds
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Horizon instability of extremal black holes
S. Aretakis · 2012
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Well-posedness for the massive wave equation on asymptotically anti-de Sitter spacetimes
G. Holzegel · 2012
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Asymptotics of solutions of the wave equation on de Sitter-Schwarzschild space
R. Melrose, A. Sá Barreto, and A. Vasy · 2008
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The black hole stability problem for linear scalar perturbations
M. Dafermos and I. Rodnianski · 2009
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The red-shift effect and radiation decay on black hole spacetimes
M. Dafermos and I. Rodnianski · 2009
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The Cauchy problem in general relativity
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Lectures on black holes and linear waves
M. Dafermos and I. Rodnianski · 2013
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Decay properties of Klein-Gordon fields on Kerr-AdS spacetimes
G. Holzegel and J. Smulevici · 2013
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Quasimodes and a lower bound on the uniform energy decay rate for Kerr-AdS spacetimes
G. Holzegel and J. Smulevici · 2013
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J. Sbierski · 2013
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Decay of linear waves on higher-dimensional Schwarzschild black holes
V. Schlue · 2013
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Exponentially growing finite energy solutions for the Klein-Gordon equation on sub-extremal Kerr spacetimes
Y. Shlapentokh-Rothman · 2013
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Quantitative mode stability for the wave equation on the Kerr spacetime
Y. Shlapentokh-Rothman · 2013
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A. Vasy · 2013
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Stability of charged rotating black holes for linear scalar perturbations
D. Civin · 2014
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M. Dafermos, I. Rodnianski, and Y. Shlapentokh-Rothman · 2014
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A scattering theory for the wave equation on Kerr black hole exteriors
M. Dafermos, I. Rodnianski, and Y. Shlapentokh-Rothman · 2014
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Quasinormal modes for Schwarzschild–AdS black holes: Exponential convergence to the real axis
O. Gannot · 2014
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J. Keir · 2014
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Unstable mode solutions to the Klein-Gordon equation in Kerr-anti-de Sitter spacetimes
D. Dold · 2015
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