Strength of the mass-inflation singularity at Kerr Cauchy horizons

Ascertain whether the null singularity produced by mass inflation at the Cauchy horizon inside rotating (Kerr-like) black holes is strong or weak, i.e., determine whether timelike and null geodesics can be extended through the singularity and characterize the corresponding geodesic behavior.

Background

In rotating black hole interiors, linear and nonlinear perturbations create an instability at the Cauchy horizon known as mass inflation, which replaces the horizon by a null singularity. Classical analyses indicate this mechanism is generic, but the precise nature of the resulting singularity has not been settled. A strong singularity prevents the extension of geodesics, while a weak singularity allows geodesics to pass through, profoundly affecting determinism and cosmic censorship.

Clarifying the strength of the mass-inflation singularity is central to understanding the global structure of rotating black hole spacetimes and the fate of observers approaching the inner horizon. It also bears on the mathematical formulation of strong cosmic censorship and the extendibility of the metric beyond the Cauchy horizon.

References

It remains uncertain whether this singularity is strong or weak, namely, whether geodesic trajectories can extend beyond it.

— Causality as a guiding principle for physics beyond General Relativity  (2510.18419 - García-Moreno, 21 Oct 2025) in Introduction

Those Einstein--Maxwell--Klein--Gordon results guide the present discussion but are not nonlinear theorems for the full scalaron potential. The robust conclusion here is that a locally non-tachyonic scalaron can supply an additional blueshift-amplified focusing contribution when it is excited and transmitted. Its nonlinear consequences, including Hawking-mass inflation and the regularity class of a possible extension, remain questions for the coupled evolution.

— Beyond the Dolgov-Kawasaki instability: Covariant scalaron stability, entropy transport, and inner horizons in f(R) gravity  (2610.11649 - Lobo et al., 8 Oct 2026) in Section 5.4, “The scalaron as a blueshifted source”