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

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