On the Physical Meaning of the Robinson-Trautman-Maxwell Fields

TL;DR

This paper explores the physical interpretation of Robinson-Trautman-Maxwell fields by analyzing their coordinate systems, identifying a velocity variable, and deriving equations of motion for the source's center of mass within the BMS group framework.

Contribution

It provides a novel interpretation of RT-Maxwell fields by linking a coordinate variable to velocity and deriving source motion equations from energy-momentum considerations.

Findings

Identified a velocity variable in RT coordinates.

Derived equations of motion for the source's center of mass.

Connected source dynamics to the BMS group structure.

Abstract

We study the Robinson-Trautman-Maxwell Fields in two closely related coordinate systems, the original Robinson-Trautman (RT) coordinates (in a more general context, often referred to as NU coordinates) and Bondi coordinates. In particular, we identify one of the RT variables as a velocity and then from the Bondi energy-momentum 4-vector, we find kinematic expressions for the mass and momentum in terms of this velocity. From these kinematic expressions and the energy-momentum loss equation we obtain surprising equations of motion for `the center of mass' of the source where the motion takes place in the four-dimensional Poincare translation sub-group of the BMS group.