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Register a new userPlane Fronted Limit of Spherical Electromagnetic and Gravitational Waves
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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.
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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.
The renewed serious interest to possible practical applications of gravitational waves is encouraging. Building on previous work, I am arguing that the strong variable electromagnetic fields are appropriate systems for the generation and detection of high-frequency gravitational waves (HFGW). The advantages of electromagnetic systems are clearly seen in the proposed complete laboratory experiment, where one has to ensure the efficiency of, both, the process of generation and the process of detection of HFGW. Within the family of electromagnetic systems, one still has a great variety of possible geometrical configurations, classical and quantum states of the electromagnetic field, detection strategies, etc. According to evaluations performed 30 years ago, the gap between the HFGW laboratory signal and its level of detectability is at least 4 orders of magnitude. Hopefully, new technologies of today can remove this gap and can make the laboratory experiment feasible. The laboratory experiment is bound to be expensive, but one should remember that a part of the cost is likely to be reimbursed from the Nobel prize money ! Electromagnetic systems seem also appropriate for the detection of high-frequency end of the spectrum of relic gravitational waves. Although the current effort to observe the stochastic background of relic gravitational waves is focused on the opposite, very low-frequency, end of the spectrum, it would be extremely valuable for fundamental science to detect, or put sensible upper limits on, the high-frequency relic gravitational waves. I will briefly discuss the origin of relic gravitational waves, the expected level of their high-frequency signal, and the existing estimates of its detectability.
Spherical gravitational wave is strictly forbidden in vacuum space in frame of general relativity by the Birkhoff theorem. We prove that spherical gravitational waves do exist in non-linear massive gravity, and find the exact solution. Further more, we find exact gravitational wave solution with a singular string by meticulous studies of familiar equation, in which the horizon becomes non-compact. We analyze the properties of the congruence of graviton rays of these wave solution. We clarify subtle points of dispersion relation, velocity and mass of graviton in massive gravity with linear perturbations. We find that the graviton ray can be null in massive gravity by considering full back reaction of the massive gravitational waves to the metric. We demonstrate that massive gravity has deep and fundamental discrepancy from general relativity, for whatever a tiny mass of the graviton.
We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves and, for generic initial data, produce a spacetime singularity at the focusing hypersurface. There is, in addition, an infinite family of regular solutions and an intriguing static geometry supported by scalar fields. Upon dimensional reduction, the theory can be viewed as an exactly solvable two-dimensional gravity model. This provides a new viewpoint on the gravitational dynamics. Finally, we comment on a simple mechanism by which short-distance corrections in the two-dimensional model can remove the singularity.
The direct detection of gravitational waves crowns decades of efforts in the modelling of sources and of increasing detectors sensitivity. With future third-generation Earth-based detectors or space-based observatories, gravitational-wave astronomy will be at its full bloom. Previously brushed-aside questions on environmental or other systematic effects in the generation and propagation of gravitational waves are now begging for a systematic treatment. Here, we study how electromagnetic and gravitational radiation is scattered by a binary system. Scattering cross-sections, resonances and the effect of an impinging wave on a gravitational-bound binary are worked out for the first time. The ratio between the scattered-wave amplitude and the incident wave can be of order $10^{-5}$ for known pulsars, bringing this into the realm of future gravitational-wave observatories. For currently realistic distribution of compact-object binaries, the interaction cross-section is too small to be of relevance.
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