Are the meaning of the two polarisations of gravitation wave arbitrary since one could choose arbitrary the axis direction? Are the meaning of the two polarisations of gravitation wave arbitrary since one could choose arbitrary the axis direction ?
I write the same in a different way : what is the meaning of the two polarisations of gravitation wave, that are shifted by an angle of 45 degrees, since one could arbitrary decide to change the absolute position of the vertical axis and the horizontal axis by making a rotation of 45 degree, thus this would change what is "+" and what is "x" polarizations ?
So how is defined the direction of the vertical axis ?
 A: They are arbitrary in the sense that you can construct a travelling gravitational wave by mixing together waves with the two polarisations and with the axes of the polarisations rotated by an arbitrary angle (but 45 degrees apart). This is in much the same way that you can construct any polarisation of a travelling electromagnetic wave by mixing together two plane polarised waves with arbitrary planes of polarisation at right angles to each other.
However, they are not arbitrary in the sense that gravitational wave sources do emit gravitational waves with definite polarisations and polarisation axes in the same way that an oscillating electric dipole produces electromagnetic waves with a definite plane of polarisation in the direction in which the charges/current is oscillating.
For example a merging binary system observed along the plane of its orbit will emit gravitational waves that are purely "plus" polarised, and one of the axes of the "plus" will align with the observed plane of the binary orbit.
It is for this reason that an "L"-shaped interferometer has differing sensitivities to the GW signals from merging binaries depending on where they are in the sky.
