Elliptic curvature estimates for linearised gravitational perturbations of Kerr in the full sub-extremal range |a|

2025/09/08 by Gabriele Benomio, Benomio, Gabriele, Rita Teixeira da Costa +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2509.06828

openalex publication_date 2025/09/08 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We consider the linearised vacuum Einstein equations around a Kerr exterior solution and present a scheme to prove elliptic L²(\mathbbS²)-estimates for the linearised curvature quantities in the equations. The scheme employs the linearised system of equations derived in the first author's doctoral thesis and applies to the full sub-extremal range of Kerr parameters 0≤ |a|

Citations

• Linear stability of Kerr black holes in the full subextremal range
• Optimal decay for solutions of the Teukolsky equation on the Kerr metric for the full subextremal range |a| < M
• A new gauge for gravitational perturbations of Kerr spacetimes II: The linear stability of Schwarzschild revisited
• A new gauge for gravitational perturbations of Kerr spacetimes I: The linearised theory
• Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes
• Construction of GCM hypersurfaces in perturbations of Kerr
• Kerr stability for small angular momentum
• The non-linear stability of the Schwarzschild family of black holes
• Boundedness and decay for the Teukolsky equation on Kerr in the full subextremal range |a|
• A general formalism for the stability of Kerr
• Effective results on uniformization and intrinsic GCM spheres in perturbations of Kerr
• Constructions of GCM spheres in perturbations of Kerr
• Linear stability of slowly rotating Kerr black holes

Cited by

• The Maxwell equations on full sub-extremal and extremal Kerr spacetimes

Related

• A new gauge for gravitational perturbations of Kerr spacetimes I: The linearised theory
• Bounds for the metric and shift vector on extreme Kerr under linear axially symmetric gravitational perturbations
• The Bounded L2 Curvature Conjecture
• The non linear perturbation of the Kerr spacetime in an external region
• On the linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge