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Equatorial null orbit in Schwarzschild spacetime

For inverse radius

y = 1/ r

and azimuth

ϕ

, a Schwarzschild null geodesic obeys

(y^{'})^{2} + y^{2} - 2 M y^{3} = \frac{1}{b ^{2}}, y^{''} + y = 3 M y^{2},

where

b = L / E

is the impact parameter.

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- Impact parameter Equatorial null orbit in Schwarzschild spacetime 27

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