On non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics

2017/10/20 by Piotr T. Chruściel, Chruściel, Piotr T., Erwann Delay +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Classical mechanics #De Sitter universe #Degeneracy (biology) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Gravitation #High Energy Physics - Theory (hep-th) #Mathematical physics #Physics #Quantum mechanics #Schwarzschild radius #Sociology #Theoretical physics #Universe #gr-qc #hep-th #math.DG

paper · pdf · doi:10.48550/arxiv.1710.07597

40 pages, 2 figures, v2: minor updates and corrections

openalex publication_date 2017/10/20 · arxiv created 2019/06/26 · arxiv updated 2019/06/27 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We prove that the TT-gauge-fixed linearised Einstein operator is non-degenerate for Riemannian Kottler ("Schwarzschild-anti de Sitter") metrics with dimension- and topology-dependent ranges of mass parameter. We provide evidence that this remains true for all such metrics except the spherical ones with a critical mass.

Citations

• Non-trivial, static, geodesically complete space-times with a negative cosmological constant II. n≥ 5
• Über die physikalischen Grundlagen der Einsteinschen Gravitationstheorie
• Fredholm operators and Einstein metrics on conformally compact manifolds

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