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

Abstract

We consider the action of exact plane gravitational waves, or pp-waves, 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 $\lambda$ 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.

arXiv comment20 pages, 18 figures, further arguments supporting the localizability of the gravitational energy are presented, published in Universe

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Cited by in corpus (10)

• The First-Order Velocity Memory Effect from Compact Binary Coalescing Sources
• The energy-momentum tensor of gravitational waves, Wyman spacetime and freely falling observers
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• The Work-Energy Relation for Particles on Geodesics in the pp-Wave Spacetimes
• Memory Effect of Gravitational Wave Pulses in PP-Wave Spacetimes
• Non-linear Plane Gravitational Waves as Space-time Defects
• Energy-momentum and angular-momentum of a gyratonic pp-waves spacetime
• On the Quantization of Burgers Vector and Gravitational Energy in the Space-Time of a Conical Defect
• Some geometrical aspects of gravitational waves using continuum mechanics analogy: State of the art and potential consequences
• Blueshift of light rays induced by gravitational wave memory effect