Quantitative mode stability for the wave equation on the Kerr-Newman spacetime

2014/05/14 by Damon Civin, Civin, Damon
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1405.3620

openalex publication_date 2014/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quantitative versions of mode stability type statements for the wave equation on Kerr-Newman black holes are proven for the full sub-extremal range. The mode stability result on the real axis is then applied to prove integrated local energy decay for solutions restricted to a bounded frequency regime. This is an important element of the proof of unrestricted boundedness and decay statements, presented in a forthcoming companion paper.

Related

• Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M
• Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: The cases |a| << M or axisymmetry
• Instability results for the wave equation in the interior of Kerr black holes
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