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

TL;DR

This work develops a unified analytical framework to study the scattering of massless fields with spin $s\le 2$ by a Schwarzschild‑type medium, realized via transformation optics. A common wave equation is derived for all spins, revealing a complex Coulomb‑like potential that induces both real and imaginary logarithmic phase corrections and governs asymptotic decay. The authors obtain a universal scattering amplitude and differential cross section across spins, express plane waves in a spin‑weighted harmonic basis, and connect the theory to feasible laboratory tests using Schwarzschild‑equivalent media. The results provide a bridge between analogue gravity experiments with photonic chips and the broader understanding of black‑hole scattering for gravitational and other massless fields, with potential implications for gravitational waves and related analog systems.

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.