Consider a weak, planar gravitational wave propagating in the z direction, written in a general Lorenz gauge [Eqs. (27.19)]. Show that by appropriate choices of new gauge-change generators that have the plane-wave form ξ_μ(t − z), one can 

(i) Keep the metric perturbation in Lorenz gauge; 

(ii) Annul

(iii) Thereby make the only nonzero components of the metric perturbation be

Equation 27.19.

Transcribed Image Text:

hxz> hyz, hzz, and h = n²h₁ ημνημε