General Formula for the Momentum Imparted to Test Particles in Arbitrary Spacetimes

TL;DR

This paper derives a general, exact formula for the momentum transferred to test particles by gravitational waves in any spacetime, extending previous approximate methods.

Contribution

It introduces a comprehensive, exact formula for gravitational wave momentum transfer applicable to arbitrary spacetimes, advancing beyond prior approximate approaches.

Findings

Provides a universal formula for gravitational wave momentum transfer.

Extends previous approximate methods to exact solutions.

Applicable to all spacetime geometries.

Abstract

Ehlers and Kundt have provided an approximate procedure to demonstrate that gravitational waves impart momentum to test particles. This was extended to cylindrical gravitational waves by Weber and Wheeler. Here a general, exact, formula for the momentum imparted to test particles in arbitrary spacetimes is presented.