Spacetime and Geometry · Problem 7.7

Cosmology — Sean Carroll

Physics — General Relativity · gravitational-wave-detector-orientation

Problem

Gravitational waves can be detected by monitoring the distance between two free flying masses. If one of the masses is equipped with a laser and an accurate clock, and the other with a good mirror, the distance between the masses can be measured by timing how long it takes for a pulse of laser light to make the round-trip journey. How would you want your detector oriented to register the largest response from a plane wave of the form ds2=−dt2+[1+Acos⁡(ω(t−z))] dx2+[1−Acos⁡(ω(t−z))] dy2+dz2 ?ds^2 = -dt^2 + [1 + A\cos(\omega(t-z))]\,dx^2 + [1 - A\cos(\omega(t-z))]\,dy^2 + dz^2\,? If the masses have a mean separation LL, what is the largest change in the arrival time of the pulses caused by the wave? What frequencies ω\omega would go undetected?

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