Plane Gravitational Waves, the Kinetic Energy of Free Particles and the Memory Effect

Abstract

It is shown that in the passage of a short burst of non-linear plane gravitational wave, the kinetic energy of free particles may either decrease or increase. The decreasing or increasing of the kinetic energy depends crucially on the initial conditions (position and velocity) of the free particle. Therefore a plane gravitational wave may extract energy from a physical system.

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

“…(12), which may be inverted to yield a µ = φ (0)(i) e (i)µ , where {a j } are the spatial components of the inertial acceleration that maintain the frame static in space-time, and are given by Eq. (13). We note the similarity of the right hand side of Eq.…”

“…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.…”

Ion traps and the memory effect for periodic gravitational waves

“…The Memory Effect of Gravitational Waves concerned, originally, the motion of test particles after the passage of a sudden burst of gravitational wave. See [1][2][3][4][5][6][7][8][9][10][11] and references therein for a non-exhaustive list. Later, the meaning of the expression was extended to include also the effect of periodic gravitational waves [12] sought for in inflationary models [13,14].…”

Scaling and conformal symmetries for plane gravitational waves

“…Recent insight into the "Memory Effect" for gravitational waves [1][2][3][4][5][6][7][8][9] was brought about by a better understanding of their symmetries. For exact plane waves the implicitly known isometry group [10][11][12][13][14] maps geodesics to geodesics and yields conserved quantities ; conversely, the latter determine the transverse motion (motion in the X-plane) of test particles in the gravitational wave background [10,15].…”