The Momentum Four-Vector in the $e\psi$N Formalism and the Angular Momentum Imparted to Test Particles by Gravitational Waves

TL;DR

This paper examines the momentum transfer and angular momentum imparted to test particles by gravitational waves, clarifying misconceptions and proposing a new interpretation within the extended pseudo-Newtonian formalism.

Contribution

It refutes the interpretation of the zero component of the momentum vector as angular momentum and offers an alternative explanation for the momentum transfer in gravitational waves.

Findings

The zero component of the momentum vector does not represent angular momentum.

A new interpretation for the momentum imparted by gravitational waves is proposed.

The formalism clarifies the nature of momentum transfer in gravitational wave interactions.

Abstract

Since gravitational waves are solutions of Einstein's field equations with a zero stress-energy tensor, the reality of these waves was questioned. To demonstrate it, the momentum imparted to test particles by such waves was evaluated. A closed form expression for this quantity was provided by Qadir and Sharif, using an extension of the pseudo-Newtonian formalism. That formalism carried with it the zero component of the momentum vector, which could not be interpreted as the energy imparted to the test particle. Sharif proposed that it may represent the angular momentum imparted to test particles by gravitational waves. In this paper it is shown that this interpretation is not valid. An alternative explanation has been provided.