The plus and cross polarizations of a gravitational wave are at 45 degree to each other. However, I find no explanation of this angle. Can somebody help?
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If you rotate gravitational wave (GW) of one polarization by 90 degrees along its axis of propagation, you get the GW of same polarization, only shifted in phase. Therefore, GW of another polarization, to be linearly independent, must be rotated between 0 and 90 degrees and 45 degrees are exactly between those two.
For comparison, if you rotate EM wave of one polarization by 180 degrees, you get EM wave of same polarization, only shifted in phase.
That's why polarizations of EM waves are at 90 degrees to each other, while polarizations of GWs are at 45 degrees to each other.
Danijel
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