The Work-Energy Relation for Particles on Geodesics in the pp-Wave Spacetimes

Abstract

A non-linear gravitational wave imparts gravitational acceleration to all particles that are hit by the wave. We evaluate this acceleration for particles in the pp-wave space-times, and integrate it numerically along the geodesic trajectories of the particles during the passage of a burst of gravitational wave. The time dependence of the wave is given by a Gaussian, so that the particles are free before and after the passage of the wave. The gravitational acceleration is understood from the point of view of a flat space-time, which is the initial and final gravitational field configuration. The integral of the acceleration along the geodesics is the analogue of the Newtonian concept of work per unit mass. Surprisingly, it yields almost exactly the variation of the non-relativistic kinetic energy per unit mass of the free particle. Therefore, the work-energy relation $\Delta K=\Delta W$ of classical Newtonian physics also holds for a particle on geodesics in the pp-wave space-times, in a very good approximation, and explains why the final kinetic energy of the particle may be smaller or larger than the initial kinetic energy.

25 pages, 7 figures, published in the JCAP

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Cited by in corpus (5)

• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• Non-linear Plane Gravitational Waves as Space-time Defects
• Memory Effect of Gravitational Wave Pulses in PP-Wave Spacetimes
• Hidden symmetries from distortions of the conformal structure
• Energy-momentum and angular-momentum of a gyratonic pp-waves spacetime