On regular rotating black holes

TL;DR

This paper rigorously analyzes the conditions for regularity in Kerr-like rotating black hole spacetimes, revealing that regularity requires violating weak energy conditions near the core.

Contribution

It provides necessary and sufficient conditions for the regularity of rotating black holes and links this regularity to energy condition violations.

Findings

Derived conditions for spacetime regularity

Linked regularity to weak energy condition violations

Clarified the nature of scalar invariants in these spacetimes

Abstract

Different proposals for regular rotating black hole spacetimes have appeared recently in the literature. However, a rigorous analysis and proof of the regularity of this kind of spacetimes is still lacking. In this note we analyze rotating Kerr-like black hole spacetimes and find the necessary and sufficient conditions for the regularity of all their second order scalar invariants polynomial in the Riemann tensor. We also show that the regularity is linked to a violation of the weak energy conditions around the core of the rotating black hole.