Test particle motion in a gravitational plane wave collision background

Abstract

Test particle geodesic motion is analysed in detail for the background spacetimes of the degenerate Ferrari-Ibañez colliding gravitational wave solutions. Killing vectors have been used to reduce the equations of motion to a first order system of differential equations which have been integrated numerically. The associated constants of the motion have also been used to match the geodesics as they cross over the boundary between the single plane wave and interaction zones.

Refraction index analysis of light propagation in a colliding gravitational wave spacetime

“…This peculiar asymmetry characterizing the behavior of null geodesics depending on the presence/absence of a y−component in the incoming 4-momentum can be associated with a different role played by the x− and y−coordinates spanning the surface of the wavefront in these spacetimes, as discussed in Ref. [27] in the case of timelike geodesics. An example of numerical integration of the orbits with p y = 0 is shown in Fig.…”

Neutrino Current in a Gravitational Plane Wave Collision Background

“…It is worth noting that once again the ∂ x direction has special properties which we have studied in terms of Papapetrou fields and Killing directions in a previous paper [6].…”

“…(which corresponds to energy-momentum conservation for the test particle [6]). A straightforward solution for the amplitudes of the wave functions is:…”

“…Explicit results are given for the degenerate solutions found by Ferrari and Ibañez [4], in which the interaction region of the colliding waves propagating along the common z direction is of Petrov type D, with a Killing-Cauchy horizon formed at a finite distance from the collision plane, after a finite time from the instant of collision. For this spacetime a careful analysis of timelike geodesics has only recently been performed [6].…”

Effect of Nut Parameter on the Analytic Extension of the Cauchy Horizon That Develop in Colliding Wave Space–times

“…The geodesic description of CGW spacetime is almost well-known by now [21,22,23,24] Any geodesic originating from the flat region fall into the singularity ( or horizon) in a finite proper time. Some geodesics remain in the incoming regions without ever crossing into the interaction region I 0 .…”