Action principle selection of regular black holes

TL;DR

This paper investigates how higher-derivative curvature invariants influence the quantum selection of regular black hole spacetimes within the Lorentzian path integral framework, revealing that some regular solutions are suppressed due to singular invariants.

Contribution

It demonstrates that including higher-derivative curvature invariants in the action can exclude certain regular black hole solutions from contributing to the quantum gravitational path integral.

Findings

Regular black hole metrics can have singular higher-derivative invariants.

Including these invariants in the action suppresses some regular solutions.

The finite action principle influences the quantum selection of spacetime geometries.

Abstract

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.