The Schwarzschild weak-deflection angle is derived to all orders from a phase-plane amplitude cubic, giving an explicit coefficient formula with convergence radius at the photon sphere.
−dy dq q=ϵsin 3 Θ −1 # dΘ.(4.28) The symmetry sin(π−Θ) = sin Θ(4.29) implies that the integrand is symmetric about closest approach. We may therefore write α= 2 Z π/2 0
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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes
The Schwarzschild weak-deflection angle is derived to all orders from a phase-plane amplitude cubic, giving an explicit coefficient formula with convergence radius at the photon sphere.