How are gravitational waves polarized?

Answer 1

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

The linear-polarization state of the CMB in a direction #nhat# can be described by a symmetric trace-free 2 × 2 tensor. https://tutor.hix.ai

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.

Gravitational Waves.pdf https://tutor.hix.ai

Additionally, please refer to https://tutor.hix.ai

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Answer 2

Evan Ashley

Unlike electromagnetic waves, which have two possible polarization states denoted as "plus" and "cross," which represent different orientations of wave oscillations, gravitational waves are not polarized.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.