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 ∆K = ∆W of classical Newtonian physics also holds for a particle on geodesics in the pp-wave spacetimes, 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.

Hidden symmetries from distortions of the conformal structure

“…Among the various studies regarding geodesic equations, a great number is devoted to the motion in a pp-wave background [27][28][29][30][31][32][33][34][35][36]. The symmetries of the pp-wave metrics have been extensively studied in several works [37][38][39].…”

Energy-momentum and angular-momentum of a gyratonic pp -waves spacetime

“…For a particle that interacts with the wave, the difference in the energy of the particle before and after the wave hits the particle, represents the energy absorbed or emitted by the particle. This difference depends on the direction of the acceleration of the gravitational field, as well on the initial conditions of the particle [25]. The peak value in Fig.…”

“…With the set of tetrads (25), the energy-momentum of the gravitational field can be obtained. In order to achieve such aim, first we calculate the non-vanishing components of T abc = e bµ e cν T a µν , reading…”

Non-linear plane gravitational waves as space-time defects

“…The memory effect is the permanent displacement of massive particles and ordinary objects of a physical system caused by the passage of a non-linear gravitational wave (although the memory effect is also considered in the context of linearised gravitational waves). In particular, the dynamical state of the massive particles is different before and after the passage of the wave [12][13][14][15], in view of the velocity memory effect. The "permanent displacement" mentioned above may be understood as a plastic deformation of the physical medium, that is constituted by massive particles, and in this sense propagating defects in metals (and crystalline lattices) and non-linear gravitational waves share relevant features.…”