# How are gravitational waves polarized?

Sep 21, 2017

The linear-polarization state of the CMB in a direction nhat can be described by a symmetric trace-free 2 × 2 tensor.
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.