Analytic formulas for capture cross-sections and photon escape angles in the quadrupolar q-metric, reducing to Schwarzschild at q=0.
Kundu, Journal of Mathematical Physics 22, 2006 (1981)
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Gravitational capture cross-section in Zipoy-Voorhees spacetimes
Analytic formulas for capture cross-sections and photon escape angles in the quadrupolar q-metric, reducing to Schwarzschild at q=0.