LIGO only measures of diagonal components of metric tensor? In a paper from Paik et al. 2016, they state (Section 3) that, a terrestrial gravitational wave (GW) detector measures only one off-diagonal component of the metric tensor.
Can anyone further expand on why this is so? From my copy of Misner, Thorne, and Wheeler, I understand that we work with a linearized theory and adopt the transverse traceless (TT) gauge, which reduces the perturbed metric to be written just in terms of 2 degrees of freedom corresponding to the two GW polarizations.
In this case, is a terrestrial detector (e.g. LIGO) not detecting two components, and they are not necessarily off-diagonal? 
Thanks
 A: It does not matter if you linearize GR or not but in transverse-traceless gauge there are only 2 polarizations ($h_+$ and $h_\times$). In linearized gravity you have the freedom to write these two polarizations as,
$$
h_{\alpha \beta}(t,z)
  =  \left( 
  \begin{array}{c c c c}
   0 & 0 & 0 & 0 \\
   0 & 1 & 0 & 0 \\
   0 & 0 & -1 & 0 \\
   0 & 0 & 0 & 0 
  \end{array}
 \right) h_+(t-z)
 + \left( 
  \begin{array}{c c c c}
   0 & 0 & 0 & 0 \\
   0 & 0 & 1 & 0 \\
   0 & 1 & 0 & 0 \\
   0 & 0 & 0 & 0 
  \end{array}
 \right) h_\times(t-z)
 \, ,$$
You may have more polarizations in a different gauge, but, eventually as you say there are only two independent DOF. Considering that the detectors response to an incoming wave is given as
$$ h = F_+h_+ + F_\times h_\times$$
So with one or two detector you cant say much. But, if you have 3 detectors you can tell the polarization of an incoming wave i.e. is it linear, circular, elliptic etc. polarized ? You can triangulate the source and tell about the skymap. 
