General Relativity: An Introduction for Physicists · Problem 11.3

Schwarzschild black holes — Hobson, Efstathiou & Lasenby

Physics · radially-moving-photons-schwarzschild

Problem

Show that the worldlines of radially moving photons in the Schwarzschild geometry are given by ct=r+2μln⁡∣r2μ−1∣+constant(outgoing photon),ct = r + 2\mu\ln\left|\frac{r}{2\mu}-1\right| + \text{constant} \qquad \text{(outgoing photon)}, ct=−r−2μln⁡∣r2μ−1∣+constant(incoming photon).ct = -r - 2\mu\ln\left|\frac{r}{2\mu}-1\right| + \text{constant} \qquad \text{(incoming photon)}.

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