Non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics: Birkhoff-type results in linearized gravity

2018/06/13 by Paul Klinger, Klinger, Paul
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.DG

paper · pdf · doi:10.48550/arxiv.1806.05023

12 pages

arxiv created 2018/06/13 · arxiv updated 2018/06/14

Abstract

We prove Birkhoff-type results showing that L² solutions of the linearized Einstein equations around Riemannian Kottler ("Schwarzschild-anti de Sitter") metrics in arbitrary dimension and horizon topology, which are not controlled by "master functions" are pure gauge. Together with earlier results this implies that the TT-gauge-fixed linearized Einstein operator for these metrics is non-degenerate for open ranges of the mass parameter.

Related

• On non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics
• Linear Stability of Schwarzschild-Anti-de Sitter spacetimes I: The system of gravitational perturbations
• Exact Schwarzschild-de Sitter black holes in a family of massive gravity models
• Linear Stability of Schwarzschild Spacetime: Decay of Metric Coefficients
• Schwarzschild manifold and non-regular coordinate transformations (A critico-historical Note)