General Relativity: An Introduction for Physicists · Problem 12.17

Further spherically symmetric geometries — Hobson, Efstathiou & Lasenby

Physics · reissner-nordstrom-charged-particle-conserved-quantity

Problem

For a particle of mass

m

and charge

e

in geodesic motion in the Reissner–Nordström geometry, show that the quantity

k = m\left(1 - \frac{2\mu}{r} + \frac{q^2}{r^2}\right)\frac{dt}{d\tau} + \frac{eq}{r}

is conserved, and interpret this result physically.