The spacetime Penrose inequality with charge and original-data rigidity

Under the stated energy, decay, and trapping hypotheses, we prove the sharp charged spacetime Penrose upper-area inequality for one-ended three-dimensional initial data with source-free electric and magnetic fields. The theorem allows arbitrary second fundamental form, nonzero ADM momentum, and disconnected boundary. Writing m for invariant ADM mass, Q for total charge magnitude, and r${}_A$ for the minimum-enclosing-area radius, the bound is m ≥ Q and $r_A\le m+\sqrt{m^2-Q^2}$. The polynomial mass bound $m\ge (r_A+Q^2/r_A)/2$ is asserted only when $r_A>Q$. When m > Q, equality under the stated connected, outermost, outer-area-minimizing future-horizon hypotheses identifies the original data as a smooth spacelike slice of dyonic Reissner–Nordström, including smooth attachment at the future horizon.