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Hi, Milton

you are right. A gravity wave distorts space-time. Usually one assumes that
the distortion is small and the metric is almost the Minkowski metric. Let
us denote the distortion by h. Squares of h are neglected. Gravity waves
are solutions to the Einstein equation inserting the distorted Minkowski
metric into Einstein's equations. To some respect, gravity waves are very
similar to electromagnetic waves. A general gravity wave is a superposition
of waves with two possible polarizations. Let us assume that the wave
propagates along the z-direction and that there is a ring of test-particles
in the x-y plane perpendicular to the propagation. If a polarized gravity
wave passes the ring of test particles, it will be squeezed in one
direction and stretched in the perpendicular direction. This specific form
of gravity waves is due to the Einstein equations. The pattern of a general
wave will be more complicated as it is a superposition of polarized waves.
But still, it will squeeze and stretch distances between particles in the
transverse direction of its propagation.

A good reference is the book by Foster and Nightingale, "A short course in
General Relativity" or this
article on LIGO.

I hope this helps you

regards, Michael

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