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

Piotr T. Chruściel (1) , Erwann Delay (2) , Paul Klinger (1)

1 Universität Wien = University of Vienna
2 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

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.

Domaines: Mathématiques [math]; Géométrie différentielle [math.DG]

Piotr T. Chruściel, Erwann Delay, Paul Klinger. On non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics. 2017. ⟨hal-01627149⟩