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.

• Received 8 May 2021
• Accepted 16 September 2021

DOI:https://doi.org/10.1103/PhysRevD.104.084072