We consider the Klein–Gordon equation on asymptotically anti-de-Sitter spacetimes subject to Neumann or Robin (or Dirichlet) boundary conditions and prove propagation of singularities along generalized broken bicharacteristics. The result is formulated in terms of conormal regularity relative to a twisted Sobolev space. We use this to show the uniqueness, modulo regularizing terms, of parametrices with prescribed $\text{b}$-wavefront set. Furthermore, in the context of quantum fields, we show a similar result for two-point functions satisfying a holographic Hadamard condition on the $\text{b}$-wavefront set.

中文翻译：

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一般边界条件和全息哈达马条件下广告时空奇点的传播

我们考虑受 Neumann 或 Robin（或 Dirichlet）边界条件影响的渐近反德西特时空上的 Klein-Gordon 方程，并证明奇点沿广义破碎双特征传播。结果是根据相对于扭曲的 Sobolev 空间的共法规律来表示的。我们用它来显示具有规定的参数的唯一性，模正则化项$\文本{b}$-波前设置。此外，在量子场的背景下，我们展示了满足全息 Hadamard 条件的两点函数的类似结果$\文本{b}$-波前设置。