Black Hole Solutions in Dark Photon Models with Higher Order Corrections

In this work, we derive new analytic, static, symmetric black hole solutions in theories involving dark photons with minimal and higher-order magnetic dipole interactions. Starting from the effective non-relativistic potential between fermions mediated by a dark photon, we derive explicit corrections to the Schwarzschild geometry induced by dark photon and spin-dependent terms. These corrections alter the metric significantly at short distances, modifying the horizon radius, Hawking temperature, photon sphere, and consequently, the black hole shadow. Employing perturbative expansions, we provide analytic expressions for the deviations from the Schwarzschild solution, highlighting an exponential suppression controlled by the dark photon mass. Our results demonstrate that higher-order magnetic dipole interactions produce distinctive spin-dependent curvature terms, amplifying gravitational effects near the horizon. These findings provide a theoretical foundation for future phenomenological tests of dark photon models through gravitational wave astronomy and black hole imaging, while highlighting dark photons' role as mediators of dark matter interactions that can influence structure formation and direct detection experiments.