General Relativity: An Introduction for Physicists · Problem 10.4

Experimental tests of general relativity — Hobson, Efstathiou & Lasenby

Physics · gr-photon-trajectory-solution

Problem

Verify that the general-relativistic equation of motion for a photon trajectory (10.9) has the solution

u = \frac{\sin\phi}{b} + \frac{3GM}{2c^2 b^2}\left(1 + \frac{1}{3}\cos 2\phi\right),

to first order in the relativistic perturbation to a straight-line path.