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

Abstract

We prove Birkhoff-type results showing that $L^2$ 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.

arXiv comment12 pages

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Cited by in corpus (1)

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