Testing the nonlinear stability of Kerr-Newman black holes

TL;DR

This study uses numerical simulations within Einstein-Maxwell theory to test the nonlinear stability of Kerr-Newman black holes across a range of parameters, finding no evidence of instability.

Contribution

First comprehensive numerical analysis of Kerr-Newman black hole stability across a broad parameter space, confirming stability without signs of nonlinear instability.

Findings

No significant horizon or spin variations observed

Quadrupolar modes depend only on the extremality ratio

Black holes remain stable under small perturbations

Abstract

The nonlinear stability of Kerr-Newman black holes (KNBHs) is investigated by performing numerical simulations within the full Einstein-Maxwell theory. We take as initial data a KNBH with mass $M$, angular momentum to mass ratio $a$ and charge $Q$. Evolutions are performed to scan this parameter space within the intervals $0\le a/M\le 0.994$ and $0\le Q/M\le 0.996$, corresponding to an extremality parameter $a/a_{\rm max}$ ($a_{\rm max} \equiv \sqrt{M^2-Q^2}$) ranging from $0$ to $0.995$. These KNBHs are evolved, together with a small bar-mode perturbation, up to a time of order $120M$. Our results suggest that for small $Q/a$, the quadrupolar oscillation modes depend solely on $a/a_{\rm max}$, a universality also apparent in previous perturbative studies in the regime of small rotation. Using as a stability criterion the absence of significant relative variations in the horizon areal radius and BH spin, we find no evidence for any developing instability.