General Relativity: An Introduction for Physicists · Problem 12.1

Further spherically symmetric geometries — Hobson, Efstathiou & Lasenby

Physics · static-diagonal-metric-4-velocity

Problem

For a general static diagonal metric, show that the 4-velocity of a perfect fluid in the spacetime must have the form

[u^\mu] = \frac{c}{\sqrt{g_{00}}}(1, 0, 0, 0).