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Perturbative derivation of Schwarzschild light deflection

Writing

y = b^{- 1} sin ϕ + Δ y

in

y^{''} + y = 3 M y^{2}

and retaining first order in

M

gives

Δ y^{''} + Δ y = \frac{3 M}{2 b ^{2}} (1 - cos 2 ϕ) .

The displacement of the outgoing zero is

4 M / b

.

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Solution