Linear stability of Kerr-Newman black holes for all subextremal parameters
In plain words
The charged, spinning Kerr-Newman solution is the most general black hole of Einstein-Maxwell theory. Its stability has resisted proof because gravitational and electromagnetic waves stay coupled and cannot be separated into simple equations.
Precise statement
For Kerr-Newman with $a^{2}+Q^{2}<M^{2}$ (Gaussian units, $G=c=1$), prove that solutions of the linearized Einstein-Maxwell equations decay to a linearized Kerr-Newman solution plus pure gauge. Numerical mode analysis finds no growing modes up to 99.999 percent of extremality (Dias, Godazgar, Santos 2015), the coupled Teukolsky and Regge-Wheeler system is derived (Giorgi 2020), and decay is proved for weak charge and slow rotation (He 2023). An answer is a proof for the full range or an unstable mode.
What would settle it
A linear stability proof covering all $a^{2} + Q^{2} < M^{2}$, or an exhibited growing mode.
Status in the literature
Unverified note
Hintz (arXiv:2609.33661, September 2026) separated the coupled spin-1 and spin-2 equations and proved the absence of real-frequency modes for all subextremal parameters; decay for the full range is open as of 2026.