Question

How are gravitational waves polarized?

Answer 1

It is a result of the symmetry in the perturbation equation that describes their origination.

Explanation:

The linear-polarization state of the CMB in a direction `nhat` can be described by a symmetric trace-free 2 × 2 tensor.
http://ned.ipac.caltech.edu/level5/Sept02/Kamionkowski/Kamion2.html

Looking at the geodesic deviation by setting first `A_"xx" = 0` then setting `A_"xy" = 0` will show that there are two distinct physical states for the wave — these are the gravitational wave polarization states. The effect of a wave in either state is to compress the geodesics in one direction while simultaneously stretching the geodesic separation in the orthogonal direction during the first half-cycle of a wave. During the second half-cycle, it switches the compression and stretching effects between the axes.

http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf

See also:
http://ned.ipac.caltech.edu/level5/Sept02/Kamionkowski/Kamion2.html