# How are gravitational waves polarized?

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SCooke Share
Sep 21, 2017

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

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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 ${A}_{\text{xx}} = 0$ then setting ${A}_{\text{xy}} = 0$ 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

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