Exact analytic rotating black-hole solutions with primary hair

Exact, analytic, asymptotically flat rotating black-hole solutions are exceedingly rare, with only a handful of examples known. Using a Kerr-Schild ansatz, we derive a multitude of exact, analytic, asymptotically flat rotating black-hole solutions within a broad class of Generalized Proca theories. These black holes differ significantly from Kerr black holes, as they possess primary hair and are non-circular, thus breaking a symmetry that vacuum black holes exhibit in General Relativity.