Analytic derivation of photon ring geometry, redshift, and travel time for a Schwarzschild black hole in an inhomogeneous pressureless plasma, with comparisons to vacuum and homogeneous plasma cases.
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Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma
Analytic derivation of photon ring geometry, redshift, and travel time for a Schwarzschild black hole in an inhomogeneous pressureless plasma, with comparisons to vacuum and homogeneous plasma cases.