Consider a system that can be covered by nearly globally Lorentz coordinates in which the Newtonian-limit constraints (25.75) are satisfied. For such a system, flesh out the details of the text’s derivation of the Newtonian limit. More specifically, do the following.

(a) Derive Eq. (25.76) for the components of the 4-velocity of a particle.

(b) Show that the geodesic equation reduces to Eq. (25.77).

(c) Show that to linear order in the metric perturbation h_αβ, the components of the Riemann tensor take the form of Eq. (25.80).

(d) Show that in the slow-motion limit the space-time-space-time components of Riemann take the form of Eq. (25.81).

Equations.

Transcribed Image Text:

gaß = nap +hap, with hap<1. (25.75a)