Fermi normal coordinates provide a standardized way to describe the effects of gravitation from the point of view of an inertial observer. These coordinates have always been introduced via perturbation expansions and were usually limited to distances
much less than the characteristic length scale set by the curvature of spacetime. For a plane gravitational wave this scale is given by its wavelength which defines the domain of validity for these coordinates known as the long-wavelength regime. The symmetry of this spacetime, however, allows us to extend Fermi normal coordinates far beyond the long-wavelength regime. Here we present an explicit construction for this long-range Fermi normal coordinate system based on the unique solution of the boundary-value problem for spacelike geodesics. The resulting formulae amount to summation of the infinite series for Fermi normal coordinates previously obtained with perturbation expansions. We also consider two closely related normal coordinate systems: optical coordinates which are built from null geodesics and wave-synchronous coordinates which are built from spacelike geodesics locked in phase with the propagating gravitational wave. The wave-synchronous coordinates yield the exact solution of Peres and Ehlers-Kundt which is globally defined. In this case, the limitation of the long-wavelength regime is completely overcome, and the system of wave-synchronous coordinates becomes valid for arbitrarily large distances. Comparison of the different coordinate systems is done by considering the motion of an inertial test mass in the field of a plane gravitational wave.
A network of large-scale laser interferometers is currently employed for searches of gravitational waves from various astrophysical sources. The frequency dependence of the dynamic response of these detectors introduces corrections to their antenna p
atterns which in principle can affect the outcome of the associated data-analysis algorithms. The magnitude of these corrections and the corresponding systematic errors have recently been estimated for searches of periodic and stochastic gravitational waves (CQG 25 (2008) 184017). However, the calculation of the detector response in that paper followed the traditional semi-rigorous approach which does not properly take into account the curved nature of spacetime. The question then arises as to whether the results will be the same if the calculation is done within the rigorous framework of general relativity. In this paper we provide such a derivation of the response of the detectors to gravitational waves. We obtain the photon propagation time from the solution of the equation for null geodesics and calculate the corresponding phase delay by solving the eikonal equation for curved spacetime. The calculations are then extended to include phase amplification from multi-beam interference in Fabry-Perot resonators which play an important role in the formation of the signal in these detectors.
Searches for gravitational wave bursts that are triggered by the observation of astronomical events require a different mode of analysis than all-sky, blind searches. For one, much more prior information is usually available in a triggered search whi
ch can and should be used in the analysis. Second, since the data volume is usually small in a triggered search, it is also possible to use computationally more expensive algorithms for tasks such as data pre-processing that can consume significant computing resources in a high data-volume un-triggered search. From the statistical point of view, the reduction in the parameter space search volume leads to higher sensitivity than an un-triggered search. We describe here a data analysis pipeline for triggered searches, called {tt RIDGE}, and present preliminary results for simulated noise and signals.
