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Further spherically symmetric geometries — Hobson, Efstathiou & Lasenby
Physics · reissner-nordstrom-radial-photon-worldlines
Problem Show that the worldlines of radially moving photons in the Reissner–Nordström geometry are given by
c t = r − r − 2 r + − r − ln ∣ r r − − 1 ∣ + r + 2 r + − r − ln ∣ r r + − 1 ∣ + constant ( outgoing ) , ct = r - \frac{r_-^2}{r_+ - r_-}\ln\left|\frac{r}{r_-} - 1\right| + \frac{r_+^2}{r_+ - r_-}\ln\left|\frac{r}{r_+} - 1\right| + \text{constant} \quad (\text{outgoing}), c t = r − r + − r − r − 2 ln r − r − 1 + r + − r − r + 2 ln r + r − 1 + constant ( outgoing ) , c t = − r + r − 2 r + − r − ln ∣ r r − − 1 ∣ − r + 2 r + − r − ln ∣ r r + − 1 ∣ + constant ( ingoing ) . ct = -r + \frac{r_-^2}{r_+ - r_-}\ln\left|\frac{r}{r_-} - 1\right| - \frac{r_+^2}{r_+ - r_-}\ln\left|\frac{r}{r_+} - 1\right| + \text{constant} \quad (\text{ingoing}). c t = − r + r + − r − r − 2 ln r − r − 1 − r + − r − r + 2 ln r + r − 1 + constant ( ingoing ) . Browse the problem library