A clarification on a common misconception about interferometric detectors of gravitational waves

The aims of this letter are two. First, to show the angular gauge-invariance on the response of interferometers to gravitational waves (GWs). In this process, after resuming for completeness results on the Transverse-Traceless (TT) gauge, where, in general, the theoretical computations on GWs are performed, we analyse the gauge of the local observer, which represents the gauge of a laboratory environment on Earth. The gauge-invariance between the two gauges is shown in its full angular and frequency dependences. In previous works in the literature this gauge-invariance was shown only in the low frequencies approximation or in the simplest geometry of the interferometer with respect to the propagating GW (i.e. both of the arms of the interferometer are perpendicular to the propagating GW). Second, as far as the computation of the response functions in the gauge of the local observer is concerned, a common misconception about interferometers is also clarified. Such a misconception purports that, as the wavelength of laser light and the length of an interferometer's arm are both stretched by a GW, no effect should be visible, invoking an analogy with cosmological redshift in an expanding universe.