Gravitational energy creation in the sandwich pp-waves collision

Abstract

This article investigates the spacetime of two colliding sandwich gravitational waves, focusing on evaluating gravitational energy before and after the collision. In the framework of the teleparallel equivalent of general relativity (TEGR), we derive a true energy–momentum tensor for the gravitational waves and integrate it over a finite region of space, obtaining analytical expressions for the energy of each wave and the resulting spacetime. Our findings reveal that the energy after the collision exceeds the pre-collision, indicating energy creation. We analyze the energy density and ‘surface energy density’ on the wavefronts, underscoring their divergence near the singularity. Additionally, we observe that the colliding waves drag observers but exert no acceleration at the collision event. This study addresses and resolves longstanding issues raised by Szekeres in his seminal work on colliding pp-waves, offering a more physically realistic framework through the local energy definition provided by TEGR. The implications for gravitational wave interactions and their energy transfer mechanisms are discussed.