Quasi-Normal Modes and Exponential Energy Decay for the Kerr-de Sitter Black Hole
By Semyon Dyatlov. 2010
133 citations recorded by the source corpus.
We provide a rigorous definition of quasi-normal modes for a rotating black hole. They are given by the poles of a certain meromorphic family of operators and agree with the heuristic definition in the physics literature. If the black hole rotates slowly enough, we show that these poles form a discrete subset of $${\mathbb C}$$ . As an application we prove that the local energy of linear waves in that background decays exponentially once orthogonality to the zero resonance is imposed.
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/3f0579ce3aebe331fa5077730f809d35cdfbf094
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In Atomic and Molecular Physics, and Optics
In Mathematical Physics
In Nuclear and High Energy Physics
Citations in the corpus
- Pseudospectrum and Black Hole Quasinormal Mode Instability (2020, background): “127502 [27] Dyatlov, S.”
- Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov) (2010, unknown): “…= x2, we obtain (4.30) ∆g0 = 4(µDµ) 2 + 2ı(n− 2 + µγ)(µDµ) + µ∆h, Now we conjugate by µ−ıσ/2+n/4 to obtain µıσ/2−n/4(∆g0 − (n− 2)2 4 − σ2)µ−ıσ/2+n/4 = 4(µDµ − σ/2− ın/4)2 + 2ı(n− 2 + µγ)(µDµ − σ/2− ın/4) + µ∆h − (n− 2)2 4 − σ2 = 4(µDµ) 2 − 4σ(µDµ) + µ∆h − 4ı(µDµ) + 2ıσ − 1 + 2ıµγ(µDµ − σ/2− ın/4).”