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

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.

arXiv comment40 pages, 2 figures, v2: minor updates and corrections

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Cited by in corpus (2)

• Non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics: Birkhoff-type results in linearized gravity
• On periodic solutions of nonlinear wave equations, including Einstein equations with a negative cosmological constant