- #1
cianfa72
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- TL;DR
- About the analysis of LIGO measurements in TT gauge coordinates
I'd like to consider again what discussed in this Gravitational wave propagation in GR.
The analysis of GWs' LIGO measurements is performed in Transverse-Traceless (TT) Gauge coordinates. Basically, in the linearized gravity model, the metric tensor field ##g_{ab}## is assumed to be in the form ##g_{ab} = \eta_{ab} + h_{ab}## (note the use of abstract index notation).
As far as I can tell, the TT gauge defines a chart in which the EFEs in vacuum transform into the wave equation ##\Box \bar h_{ab}## for the tensor field ##\bar h_{ab}##. The latter is defined as $$\bar h_{ab} = h_{ab} - \frac {1} {2} \eta_{ab}h^c_c$$ So far so good.
Matematically, the wave equation above has for instance plane wave solutions. They are wave solutions in TT gauge coordinates.
As far as I understood, in LIGO measurement analysis, the arms of the interferometer are taken as "at rest" in TT coordinates (i.e. the worldlines of the arm's worldsheets have constant spacelike coordinates and varying timelike coordiante).
My questions: Why the above holds true and is the solution in wave form an invariant fact ?
The analysis of GWs' LIGO measurements is performed in Transverse-Traceless (TT) Gauge coordinates. Basically, in the linearized gravity model, the metric tensor field ##g_{ab}## is assumed to be in the form ##g_{ab} = \eta_{ab} + h_{ab}## (note the use of abstract index notation).
As far as I can tell, the TT gauge defines a chart in which the EFEs in vacuum transform into the wave equation ##\Box \bar h_{ab}## for the tensor field ##\bar h_{ab}##. The latter is defined as $$\bar h_{ab} = h_{ab} - \frac {1} {2} \eta_{ab}h^c_c$$ So far so good.
Matematically, the wave equation above has for instance plane wave solutions. They are wave solutions in TT gauge coordinates.
As far as I understood, in LIGO measurement analysis, the arms of the interferometer are taken as "at rest" in TT coordinates (i.e. the worldlines of the arm's worldsheets have constant spacelike coordinates and varying timelike coordiante).
My questions: Why the above holds true and is the solution in wave form an invariant fact ?
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