(ed.). Gravitational waves (IOP, 2001)(422s).

Exercises for chapter 2 232. Show that, in the limit where L is small compared to the wavelength ofthe gravitational wave, the derivative of the return time is the derivativeof the excess proper distance δL = Lh+ xx(t)cos2 θ for small L. Makesure you know how to interpret the factor of cos 2 θ.3. Examine the limit of the three-term formula when the gravitational waveis travelling along the x-axis too (θ =± π 2): what happens to light goingparallel to a gravitational wave?(b) Derive the two-term formula governing the delays induced by gravitationalwaves on a signal transmitted only one-way, for example from a pulsar toEarth.(c) A frequently asked question is: if gravitational waves alter the speed of light,as we seem to have used here, and if they move the ends of an interferometercloser and further apart, might these effects not cancel, so that there wouldbe no measurable effects on light? Answer this question. You may want toexamine the calculation above: did we make use of the changing distancebetween the ends, and why or why not?(d) Show that the Riemann tensor is gauge-invariant in linearized theory.