Electromagnetic perturbations in Schwarzschild spacetime reduce to a Helmholtz equation with a derived position- and frequency-dependent refractive index encoding gravitational redshift, curvature, and angular momentum.
Chandrasekhar, The Mathematical Theory of Black Holes, Clarendon Press, Oxford (1983)
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Electromagnetic wave propagation in static black hole spacetimes: an effective refractive index description in Schwarzschild geometry
Electromagnetic perturbations in Schwarzschild spacetime reduce to a Helmholtz equation with a derived position- and frequency-dependent refractive index encoding gravitational redshift, curvature, and angular momentum.