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.

中文翻译：

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关于黎曼 Schwarzschild-anti de Sitter 度量的非简并性

我们证明 $TT$-gauge-fixed 线性化爱因斯坦算子对于 Riemannian Kottler（“Schwarzschild-anti de Sitter”）度量是非退化的，其质量参数范围与尺寸和拓扑相关。我们提供的证据表明，除了具有临界质量的球形指标外，所有此类指标仍然如此。