= (4) (a) Consider a nearly Lorentz spacetime with metric guv = Nuv + huv, with huv the small metric deviation as we discussed. Find the linearized Riemann tensor components as we did in lecture, and show that these are invariant (to first order in the metric deviation) under gauge transformations huv + huv + &u,v Evim, just as we did in lecture. Construct the relevant contractions of these and find the Einstein tensor components, expressing these in terms of the trace reverse huv = hhv que h, where h is the trace of the metric deviation. Show that in the Lorentz gauge, (a), = 0, the linearized field equations are aroua = = -16. T (b) Now consider the local energy/momentum conservation condition, (Tab). = 0. Show that these are inconsistent with the linearized field equations from part (a). Is this a problem? What is the order of this inconsistency, in terms of the small metric deviation? What is this telling you about the linearized field equations and the motion of matter? = B =