Advances in Theoretical and Mathematical Physics
Volume 23 (2019)
On non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics
Pages: 1215 – 1269
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.
The research of PTC was supported in part by the Austrian Research Fund (FWF), Project P29517-N27, and by the Polish National Center of Science (NCN) under grant 2016/21/B/ST1/00940. ED was supported by the grant ANR-17-CE40-0034 of the French National Research Agency ANR (project CCEM). PK was supported by a uni:docs grant of the University of Vienna.
Published 12 February 2020