General Relativity: An Introduction for Physicists · Problem 17.8

Linearised general relativity — Hobson, Efstathiou & Lasenby

Physics · plane-gravity-waves-non-physical-k-squared-nonzero

Problem

From your answer to Exercise 17.7, show that for

k^2 \neq 0

one requires

R_{\sigma\mu\nu\rho} = 0

. Hence show that this case does not correspond to a physical wave but merely a periodic oscillation of the coordinate system.