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

TL;DR

This paper presents a unified analytical approach to study the scattering of massless particles with arbitrary spin by Schwarzschild-type black holes, revealing the role of complex potentials and providing testable predictions for electromagnetic wave experiments.

Contribution

It introduces a unified equation for scattering analysis and derives a general differential cross section applicable to all considered particle types.

Findings

Complex potential induces phase shifts in wave scattering.

Imaginary part of potential explains wave decay.

Derived analytical expression for differential cross section.

Abstract

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.