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Register a new userOn the round-trip time for a photon propagating in the field of a plane gravitational wave
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Authors
Malik Rakhmanov
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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 patterns 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.
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The propagation of free electromagnetic radiation in the field of a plane gravitational wave is investigated. A solution is found one order of approximation beyond the limit of geometrical optics in both transverse--traceless (TT) gauge and Fermi Normal Coordinate (FNC) system. The results are applied to the study of polarization perturbations. Two experimental schemes are investigated in order to verify the possibility to observe these perturbations, but it is found that the effects are exceedingly small.
In this paper, we study the polarization of a gravitational wave (GW) emitted by an astrophysical source at a cosmic distance propagating through the Friedmann-Lema^itre-Robertson-Walk universe. By considering the null geodesic deviations, we first provide a definition of the polarization of the GW in terms of the Weyl scalars with respect to a parallelly-transported frame along the null geodesics, and then show explicitly that, due to different effects of the expansion of the universe on the two polarization modes, the so-called + and $times$ modes, the polarization angle of the GW changes generically, when it is propagating through the curved background. By direct computations of the polarization angle, we show that different epochs, radiation-, matter- and $Lambda$-dominated, have different effects on the polarization. In particular, for a GW emitted by a binary system, we find explicitly the relation between the change of the polarization angle $|Delta varphi|$ and the redshift $z_s$ of the source in different epochs. In the $Lambda$CDM model, we find that the order of $|Delta varphi|{eta_0 F}$ is typically $O(10^{-3})$ to $O(10^3)$, depending on the values of $z_s$, where $eta_0$ is the (comoving) time of the current universe, and $FequivBig(frac{5}{256}frac{1}{tau_{obs}}Big)^{3/8}left(G_NM_cright)^{-5/8}$ with $tau_{obs}$ and $M_c$ being, respectively, the time to coalescence in the observers frame and the chirp mass of the binary system.
Bialynicki-Birula and Charzynski [1] argued that the gravitational wave emitted during the merger of a black hole binary may trap particles. In this Letter we amplify their statement by describing particle motion in the wave proposed by Lukash [2] to study anisotropic cosmological models. Bounded geodesics (found both analytically and numerically) arise when the wave is of Bianchi type VI. Their symmetries are identified.
Time shifting the outputs of Gravitational Wave detectors operating in coincidence is a convenient way to estimate the background in a search for short duration signals. However this procedure is limited as increasing indefinitely the number of time shifts does not provide better estimates. We show that the false alarm rate estimation error saturates with the number of time shifts. In particular, for detectors with very different trigger rates this error saturates at a large value. Explicit computations are done for 2 detectors, and for 3 detectors where the detection statistic relies on the logical ``OR of the coincidences of the 3 couples in the network.
The geometry of twisted null geodesic congruences in gravitational plane wave spacetimes is explored, with special focus on homogeneous plane waves. The role of twist in the relation of the Rosen coordinates adapted to a null congruence with the fundamental Brinkmann coordinates is explained and a generalised form of the Rosen metric describing a gravitational plane wave is derived. The Killing vectors and isometry algebra of homogeneous plane waves (HPWs) are described in both Brinkmann and twisted Rosen form and used to demonstrate the coset space structure of HPWs. The van Vleck-Morette determinant for twisted congruences is evaluated in both Brinkmann and Rosen descriptions. The twisted null congruences of the Ozsvath-Schucking,`anti-Mach plane wave are investigated in detail. These developments provide the necessary geometric toolkit for future investigations of the role of twist in loop effects in quantum field theory in curved spacetime, where gravitational plane waves arise generically as Penrose limits; in string theory, where they are important as string backgrounds; and potentially in the detection of gravitational waves in astronomy.
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