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I've gone to a conference dealing with the recent detection of gravitational waves (dated end of 2015). I then learnt that there are several interferometers accross the world.

The principle of detection is interferometry along two long arms making a 90° angle. The arms are in a common 2D plane. What was presented is that when a gravitational wave pass through the device, the arms stretch or contract by a certain amount of deformation that is measureable.

Does it mean that the deformation is measured only along this axle and thus with one interferometer it is not possible to get all variations of the $g_{\mu\nu}$ metric tensor but only $g_{ij}$ with $i=1,2$ ?

If one want other components another VIRGO/LIGO interferometer is necessary. And this second one must be oriented in another plane and another directions. Is that sounds OK or do I miss some points ?

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Yeah, that's pretty much it.

(Moreover, like light, gravitational waves have two polarizations, usually denoted $+$ and $×$, with deformations along those axes, and each LIGO detector is also incapable of detecting $×$ waves when its arms are aligned along $+$. For astronomical sources this is less important, as we don't expect a particular polarization from a random source in the sky, but the effect is still there.)

This directional sensitivity is one of the main reasons why people are building more detectors, including a new detector in India and links to the existing VIRGO facilities. (The other reason being, of course, that more detectors allow for better coincidence detection, so less chances of spurious signals, as well as a better ability to pinpoint the spatial origin of the signals.)

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