We elaborate on the role of higher-derivative curvature invariants as a quantum selection mechanism of regular spacetimes in the framework of the Lorentzian path integral approach to quantum gravity. We show that for a large class of black hole metrics prominently regular there are higher-derivative curvature invariants which are singular. If such terms are included in the action, according to the finite action principle applied to a higher-derivative gravity model, not only singular spacetimes but also some of the regular ones do not seem to contribute to the path integral.

中文翻译：

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规则黑洞的作用原理选择

我们在洛伦兹路径积分方法的量子引力框架中详细阐述了高导曲率不变量作为规则时空的量子选择机制的作用。我们表明，对于一大类显着规则的黑洞度量，存在奇异的高导数曲率不变量。如果将这些项包含在动作中，根据应用于高导引力模型的有限作用原理，不仅奇异时空，而且一些规则时空似乎对路径积分没有贡献。