The Klein-Gordon equation is solved in the curved background spacetime created by a dispersive gravitational wave. Unlike solutions of perturbed Einstein equations in vacuum, dispersive gravitational waves do not travel exactly at the speed of light. As a consequence, the gravitational wave can resonantly exchange energy with scalar massive particles. Some details of the resonant interaction are displayed in a calculation demonstrating how relativistic particles (modeled by the Klein-Gordon equation), feeding on such gravitational waves, may be driven to extreme energies.

• Received 21 December 2019
• Revised 18 February 2020
• Accepted 26 February 2020

DOI:https://doi.org/10.1103/PhysRevD.101.063010