Stable Rotating Regular Black Holes

TL;DR

This paper introduces a new rotating regular black hole model with a stable inner horizon, avoiding typical instabilities and singularities, while closely mimicking Kerr black holes externally, offering a promising candidate for future observational tests.

Contribution

The paper proposes a novel rotating regular black hole metric with a stable inner horizon, combining two regularization strategies and avoiding common stability and causality issues.

Findings

Inner horizon has zero surface gravity, ensuring stability against mass inflation.

The metric closely resembles Kerr black holes externally, with notable deviations at high spin.

The model is free from closed timelike curves and other problematic Kerr features.

Abstract

We present a rotating regular black hole whose inner horizon has zero surface gravity for any value of the spin parameter, and is therefore stable against mass inflation. Our metric is built by combining two successful strategies for regularizing singularities, i.e. by replacing the mass parameter with a function of $r$ and by introducing a conformal factor. The mass function controls the properties of the inner horizon, whose displacement away from the Kerr geometry's inner horizon is quantified in terms of a parameter $e$; while the conformal factor regularizes the singularity in a way that is parametrized by the dimensionful quantity $b$. The resulting line element not only avoids the stability issues that are common to regular black hole models endowed with inner horizons, but is also free of problematic properties of the Kerr geometry, such as the existence of closed timelike curves. While the proposed metric has all the phenomenological relevant features of singular rotating black holes -- such as ergospheres, light ring and innermost stable circular orbit -- showing a remarkable similarity to a Kerr black hole in its exterior, it allows nonetheless sizable deviations, especially for large values of the spin parameter $a$. In this sense, the proposed rotating "inner-degenarate" regular black hole solution is not only amenable to further theoretical investigations but most of all can represent a viable geometry to contrast to the Kerr one in future phenomenological tests.