Electrodynamics effects on colliding gravitational waves background

The degenerate Ferrari-Ibanez solution describes the collision of plane gravitational waves with aligned linear polarization, within the interaction region, the solution is Schwarzschild-like metric, which impels us to be more interesting to analyze the collision process. In this paper, we have considered the electrodynamics effects on the colliding gravitational waves background. Moreover, we have calculated explicitly out the solutions of the electromagnetic waves produced by the plane gravitational wave and the colliding region of plane gravitational waves perturbing a weak magnetic field background. We also work out the solutions of these electromagnetic waves after crossing out a weak magnetic field background.

Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency νg is much smaller than the particle's orbital one nb. We make neither a priori assumptions about the direction of the wavevector k nor on the orbital configuration of the particle. While the semi-major axis a is left unaffected, the eccentricity e, the inclination I, the longitude of the ascending node Ω, the longitude of pericenter ϖ and the mean anomaly ℳ undergo non-vanishing long-term changes of the form dΨ/dt=F(Kij;e,I,Ω,ω),Ψ=e,I,Ω,ϖ,M, where Kij, i,j=1,2,3 are the coefficients of the tidal matrix K. Thus, in addition to the variations of its orientation in space, the shape of the orbit would be altered as well. Strictly speaking, such effects are not secular trends because of the slow modulation introduced by K and by the orbital elements themselves: they exhibit peculiar long-term temporal patterns which would be potentially of help for their detection in multidecadal analyses of extended data records of planetary observations of various kinds. In particular, they could be useful in performing independent tests of the inflation-driven ultra-low gravitational waves whose imprint may have been indirectly detected in the Cosmic Microwave Background by the Earth-based experiment BICEP2. Our calculation holds, in general, for any gravitationally bound two-body system whose orbital frequency nb is much larger than the frequency νg of the external wave, like, e.g., extrasolar planets and the stars orbiting the Galactic black hole. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.

Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency νg is much smaller than the particle's orbital one nb. We make neither a priori assumptions about the direction of the wavevector k nor on the orbital configuration of the particle. While the semi-major axis a is left unaffected, the eccentricity e, the inclination I, the longitude of the ascending node Ω, the longitude of pericenter ϖ and the mean anomaly ℳ undergo non-vanishing long-term changes of the form dΨ/dt=F(Kij;e,I,Ω,ω),Ψ=e,I,Ω,ϖ,M, where Kij, i,j=1,2,3 are the coefficients of the tidal matrix K. Thus, in addition to the variations of its orientation in space, the shape of the orbit would be altered as well. Strictly speaking, such effects are not secular trends because of the slow modulation introduced by K and by the orbital elements themselves: they exhibit peculiar long-term temporal patterns which would be potentially of help for their detection in multidecadal analyses of extended data records of planetary observations of various kinds. In particular, they could be useful in performing independent tests of the inflation-driven ultra-low gravitational waves whose imprint may have been indirectly detected in the Cosmic Microwave Background by the Earth-based experiment BICEP2. Our calculation holds, in general, for any gravitationally bound two-body system whose orbital frequency nb is much larger than the frequency νg of the external wave, like, e.g., extrasolar planets and the stars orbiting the Galactic black hole. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.