The linear stability of the Schwarzschild solution to gravitational perturbations

2016/01/25 by Mihalis Dafermos, Gustav Holzegel, Igor Rodnianski · 189 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Classical mechanics #Deriving the Schwarzschild solution #General relativity #Gravitation #Kerr metric #Mathematical physics #Null (SQL) #Physics #Pulsars and Gravitational Waves Research #Schwarzschild metric #Schwarzschild radius #gr-qc #math-ph #math.AP #math.DG #math.MP

paper · pdf · doi:10.4310/acta.2019.v222.n1.a1

published in Acta Mathematica 222(1), 1-214 (Mittag-Leffler Institute) · 146 pages, 4 figures

arxiv created 2016/01/25 · openalex publication_date 2019/01/01 · arxiv updated 2019/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

the linear stability of the schwarzschild solution 3 13.4. Boundedness estimates for the ingoing shear

Citations

• On the global stability of the wave-map equation in Kerr spaces with small angular momentum
• Ultimately Schwarzschildean Spacetimes and the Black Hole Stability Problem
• Gravitational Field of a Particle
• Maximal Extension of Schwarzschild Metric
• Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
• An Approach to Gravitational Radiation by a Method of Spin Coefficients
• Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior
• Semi-global existence and convergence of solutions of the Robinson-Trautman (2-dimensional Calabi) equation
• Stability of a Schwarzschild Singularity
• Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric

Cited by

• Mode Stability for the Teukolsky Equation on Extremal and Subextremal Kerr Spacetimes
• The Linear Stability of the Schwarzschild Solution to Gravitational Perturbations in the Generalised Wave Gauge
• Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric