Kerr–Newman (charged) Angular Momentum Penrose inequality

Establish the charged extension of the Angular Momentum Penrose Inequality: for asymptotically flat initial data carrying electric charge Q, determine that the ADM mass satisfies M_ADM ≥ sqrt(A/(16π) + 4π J^2/A + Q^2/4), and prove that equality is achieved precisely by Kerr–Newman initial data.

Background

The paper proves an angular-momentum version of the Penrose inequality for axisymmetric vacuum initial data without charge, matching Kerr in the equality case. A natural extension includes electric charge, where Kerr–Newman is the expected saturating solution. The authors present this as a conjectural generalization involving an additional Q-dependent term.

Including charge would broaden the applicability of the inequality to electrovacuum settings and unify mass–area–angular momentum relations consistent with known exact solutions.

References

Conjecture [Kerr-Newman Extension] For initial data with electric charge $Q$: \begin{equation} M_{ADM} \geq \sqrt{\frac{A}{16\pi} + \frac{4\pi J2}{A} + \frac{Q2}{4} \end{equation} saturated by Kerr-Newman.

— Angular Momentum Penrose Inequality (2512.06918 - Xu, 7 Dec 2025) in Section “Extensions and Open Problems”, Subsection “Charged Black Holes”