Scattering of massless waves with arbitrary spin: a unified analysis for Schwarzschild-type medium black holes

A unified equation is employed to analytically investigate the scattering of massless spin particles by a Schwarzschild-type medium black hole. It is found that for spin particles, curved spacetime induces an effective complex potential analogous to a Coulomb field. While the real part of this potential contributes a real logarithmic term to the phase, the imaginary part gives rise to a corresponding imaginary logarithmic term. Crucially, this imaginary term is precisely responsible for generating the correct asymptotic decay of the wave function. From this framework, a unified analytical expression for the differential cross section is derived, applicable to all particle types considered. Given the successful fabrication of a Schwarzschild-equivalent medium via transformation optics, our theoretical scattering predictions can be tested experimentally by transmitting plane electromagnetic waves through such a structure. Insights gained from these experiments could, in turn, shed light on the scattering of other massless fields (e.g., gravitational waves) by actual black holes.