Abstract
The cosmic strings(CSs) may be one important source of gravitational waves(GWs), and it has been intensively studied due to its special properties such as the cylindrical symmetry. The CSs would generate not only usual continuous GW, but also impulsive GW that brings more concentrated energy and consists of different GW components broadly covering low-, intermediate- and high-frequency bands simultaneously. These features might underlie interesting electromagnetic(EM) response to these GWs generated by the CSs. In this paper, with novel results and effects, we firstly calculate the analytical solutions of perturbed EM fields caused by interaction between impulsive cylindrical GWs (would be one of possible forms emitted from CSs) and background celestial high magnetic fields or widespread cosmological background magnetic fields, by using rigorous Einstein - Rosen metric. Results show: perturbed EM fields are also in the impulsive form accordant to the GW pulse, and asymptotic behaviors of the perturbed EM fields are fully consistent with the asymptotic behaviors of the energy density, energy flux density and Riemann curvature tensor of corresponding impulsive cylindrical GWs. The analytical solutions naturally give rise to the accumulation effect which is proportional to the term of distance^1/2, and based on it, we for the first time predict potentially observable effects in region of the Earth caused by the EM response to GWs from the CSs.
Highlights
Over the past century, direct detection of gravitational waves (GWs) has been regarded as one of the most rigorous and ultimate tests of general relativity, and it has always been deemed as of significant urgency and attracting extensive interest, by use of various observation schemes aiming on multifarious sources
In this paper we study the perturbed EM fields caused by the interaction between the EM system and the impulsive cylindrical GWs which could be emitted from the cosmic strings (CSs) and propagate through the background magnetic field [39,40]; based on the rigorous Einstein–Rosen metric [41,42], analytical solutions of this perturbed EM fields are obtained, by solving second order non homogeneous partial differential equation groups
In the frame of general relativity, based upon the electrodynamical equations in curved spacetime, utilizing the d’Alembert formula and relevant approaches, the analytical solutions Ey(1)(x, t) and Bz(1)(x, t) of the impulsive EM fields, perturbed by cylindrical GW pulses propagating through a background magnetic field are obtained
Summary
Direct detection of gravitational waves (GWs) has been regarded as one of the most rigorous and ultimate tests of general relativity, and it has always been deemed as of significant urgency and attracting extensive interest, by use of various observation schemes aiming on multifarious sources. J. C (2014) 74:2998 cylindrical GWs for many reasons: the EM systems (natural or in laboratory) widely occur (e.g. celestial and cosmological background magnetic fields); the GW and EM signals have identical propagating velocity, leading to a spatial accumulation effect [36,37,38]; the EM system is generally sensitive to the GWs in a very wide frequency range (especially suitable to the impulsive form because the pulse comprises different GW components among broad frequency bands), and so on. From the solutions, these impulsive peaks of perturbed EM fields are found to propagate outwards from the symmetrical axis of the CS, with their wavefronts following a cylindrical manner (see Fig. 3), and their levels gradually increase during this propagation process (due to the accumulation effect, which will be discussed later in this paper).
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