Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 5

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

Pages: 1215 – 1269

DOI: https://dx.doi.org/10.4310/ATMP.2019.v23.n5.a2

Authors

Piotr T. Chruściel (Faculty of Physics and Erwin Schrödinger Institute, University of Vienna, Austria)

Erwann Delay (Laboratoire de mathématiques d’Avignon, CNRS, Marseille, France; and Erwin Schrödinger Institute, University of Vienna, Austria)

Paul Klinger (Faculty of Physics and Erwin Schrödinger Institute, University of Vienna, Austria)

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.

Full Text (PDF format)

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