(a) Show that the “infinitesimal” coordinate transformation (25.87) produces the change (25.88) of the linearized metric perturbation and that it leaves the Riemann tensor (25.80) unchanged.

(b) Exhibit a differential equation for the ξ^α that brings the metric perturbation into gravitational Lorenz gauge [i.e., that makes h_μν^new obey the Lorenz gauge condition (25.89)].

(c) Show that in gravitational Lorenz gauge, the Einstein field equation (25.86) reduces to Eq. (25.90).

Equations.

Transcribed Image Text:

Rapys == (has, By (has, py+hpy, as - hay, ps-hps, ay). (25.80)