A Poynting theorem formulation for the gravitational wave stress pseudo tensor

TL;DR

This paper presents a straightforward, exact derivation of a Poynting-like conservation equation for gravitational waves, linking stress-energy propagation to source reactions, and confirms the pseudo tensor aligns with previous complex methods.

Contribution

It introduces a simple, physical derivation of the gravitational wave stress pseudo tensor, matching more complex results and clarifying energy flow in gravitational radiation.

Findings

Derivation of an exact Poynting-style equation for gravitational waves.

Confirmation that the pseudo tensor agrees with prior complex calculations.

Insight into the radiation reaction force in gravitational wave propagation.

Abstract

A very simple and physical derivation of the conservation equation for the propagation of gravitational radiation is presented. The formulation is exact. The result takes the readily recognisable and intuitive form of a Poynting-style equation, in which the outward propagation of stress-energy is directly related to the volumetric equivalent of a radiation reaction force acting back upon the sources, including the purely gravitational contribution to the sources. Upon averaging, the emergent pseudo tensor for the gravitational radiation is in exact agreement with that found by much more labour-intensive methods.