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Register a new userOn the propagation of electromagnetic radiation in the field of a plane gravitational wave
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Enrico Montanari
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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.
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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.
In this review paper we investigate the connection between gravity and electromagnetism from Faraday to the present day. The particular focus is on the connection between gravitational and electromagnetic radiation. We discuss electromagnetic radiation produced when a gravitational wave passes through a magnetic field. We then discuss the interaction of electromagnetic radiation with gravitational waves via Feynman diagrams of the process $graviton + graviton to photon + photon$. Finally we review recent work on the vacuum production of counterpart electromagnetic radiation by gravitational waves.
We demonstrate how plane fronted waves with colliding wave fronts are the asymptotic limit of spherical electromagnetic and gravitational waves. In the case of the electromagnetic waves we utilize Batemans representation of radiative solutions of Maxwells vacuum field equations. The gravitational case involves a novel form of the radiative Robinson--Trautman solutions of Einsteins vacuum field equations.
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.
The behaviour of a test electromagnetic field in the background of an exact gravitational plane wave is investigated in the framework of Einsteins general relativity. We have expressed the general solution to the de Rham equations as a Fourier-like integral. In the general case we have reduced the problem to a set of ordinary differential equations and have explicitly written the solution in the case of linear polarization of the gravitational wave. We have expressed our results by means of Fermi Normal Coordinates (FNC), which define the proper reference frame of the laboratory. Moreover we have provided some gedanken experiments, showing that an external gravitational wave induces measurable effects of non tidal nature via electromagnetic interaction. Consequently it is not possible to eliminate gravitational effects on electromagnetic field, even in an arbitrarily small spatial region around an observer freely falling in the field of a gravitational wave. This is opposite to the case of mechanical interaction involving measurements of geodesic deviation effects. This behaviour is not in contrast with the principle of equivalence, which applies to arbitrarily small region of both space and time.
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