Rotation overcharges vectorized black holes
A charged black hole has a ceiling: extremality bounds the charge that a given mass and spin can support. Vector hair has so far only lowered it. In the Einstein--Maxwell--Vector (EMV) model, where a massless vector field couples nonminimally to the electromagnetic invariant, the spherically symmetric vectorized Reissner--Nordström black holes are strictly undercharged: vector hair is paid for in charge. Whether this ceiling is a property of the vector field or merely of spherical symmetry has remained open, because spherical symmetry hides the hair's mass as well: its Komar mass vanishes identically and the exact identity $M_V=2Ω_HJ_V$ degenerates to $0=0$. Rotation lifts both degeneracies at once. We construct the rotating solutions of the model, the first in this setting, and find that the hair's mass is not a free parameter but a second-order invariant of the rotational response, fixed by $M_V=2Ω_HJ_V$. Above a coupling threshold the ceiling gives way: the domain of existence crosses the extremal Kerr--Newman bound, reaching $q=Q/M>1$ with $q^2+χ^2$ up to $1.84$, while at $α=5$ the maximum charge stays below it. The shadow is where the hair becomes visible. At $(q,χ)=(0.9947,0.10)$, near the extremal bound, the hair contributes an ellipticity of $8.30\%$, against $0.44\%$ from the charge and $0.06\%$ from rotation --- a factor of $19$ that charging a Kerr black hole cannot mimic; at the overcharged solution $(q,χ)=(1.2527,0.10)$ the total ellipticity reaches $25.6\%$. Whether the branch is ghost-free remains open, but the existing no-go criteria do not settle it: they assume a background and a dispersion relation that do not hold here.