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 (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 hxz hyz, hzz, and h nh

Question: 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

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.

hxz> hyz, hzz, and h = nh

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