Can black holes have Euclidean cores?

TL;DR

This paper explores the possibility of Euclidean cores within black holes, analyzing solutions in classical and higher derivative gravity theories, and introduces a smooth orbifold alternative with a space-like boundary inside the horizon.

Contribution

It demonstrates how Euclidean cores can be incorporated into black hole solutions and shows that higher derivative terms enable the weak energy condition to be satisfied.

Findings

Euclidean cores lead to finite, continuous energy densities and pressures.

Higher derivative gravity theories satisfy the weak energy condition.

A smooth orbifold construction offers an alternative with a space-like boundary.

Abstract

The search for regular black hole solutions in classical gravity leads us to consider a core of Euclidean signature in the interior of a black hole. Solutions of Lorentzian and Euclidean general relativity match in such a way that energy densities and pressures of an isotropic perfect fluid form are everywhere finite and continuous. Although the weak energy condition cannot be satisfied for these solutions in general relativity, it can be when higher derivative terms are added. A numerical study shows how the transition becomes smoother in theories with more derivatives. As an alternative to the Euclidean core, we also discuss a closely related time dependent orbifold construction with a smooth space-like boundary inside the horizon.