The Kerr–Newman extension of the angular-momentum Penrose inequality

Consider initial data satisfying the appropriate energy conditions, with horizon area $A$, angular momentum $J$, and electric charge $Q$. Kerr–Newman extension conjecture. The ADM mass should satisfy

$$M_{\mathrm{ADM}} \geq \sqrt{\frac{A}{16\pi} + \frac{4\pi J^2}{A} + \frac{Q^2}{4}},$$

with equality for Kerr–Newman spacetime. This is the full charged-and-rotating extension; the source notes that the complete Kerr–Newman case remains conjectural while pure rotation and pure charge cases are treated separately.