Variations of the Energy of Free Particles in the pp-Wave Spacetimes

Abstract

We consider the action of exact plane gravitational waves, or ppwaves, on free particles. The analysis is carried out by investigating the variations of the geodesic trajectories of the particles, before and after the passage of the wave. The initial velocities of the particles are non-vanishing. We evaluate numerically the kinetic energy per unit mass of the free particles, and obtain interesting, quasi-periodic behaviour of the variations of the kinetic energy with respect to the width λ of the gaussian that represents the wave. The variation of the energy of the free particle is expected to be exactly minus the variation of the energy of the gravitational field, and therefore provides an estimation of the local variation of the gravitational energy. The investigation is carried out in the context of short bursts of gravitational waves, and of waves described by normalised gaussians, that yield impulsive waves in a certain limit.

The work-energy relation for particles on geodesics in the pp-wave spacetimes

“…In the analysis of the trajectories and velocities of free particles in the presence of pp-waves (the particles are understood to be free before and after the passage of the wave), we have found that the final kinetic energy of the free particles may be smaller or larger than the initial values [13,14], and also that the final angular momentum of the particle may be smaller or larger in magnitude than the initial values [15]. At first sight it might sound strange that the particle loses kinetic energy, most probably by transferring this energy to the wave.…”

The Energy–Momentum Tensor of Gravitational Waves, Wyman Spacetime, and Freely Falling Observers

“…In ref. [], they study the variation of the energy of free particles under a ‐wave spacetime and, in ref. [], they present the exact form of the energy of the wave as measured by a set of static observers.…”

On the quantization of Burgers vector and gravitational energy in the space-time of a conical defect

“…This vector will be assumed to be the multiple of an integer in section IV. Using the tetrads (20), the Burgers vector may be calculated trivially by choosing the contour as an orthogonal circle around the longitudinal z axis, obtaining…”

“…One of the most interesting results is that the particle extracts a discrete amount of energy of the defect. The possibility that the energy (and also angular momentum) acquired by the particle comes from the gravitational field had already been contemplated in the case of a particle interacting with a gravitational wave [20,21].…”