The Gravitational Field of a Radiating Electromagnetic Dipole

TL;DR

This paper investigates how a time-varying electromagnetic dipole influences the surrounding gravitational field by deriving the metric perturbations and identifying angular momentum conservation laws in a Minkowski background.

Contribution

It provides a detailed calculation of the gravitational field generated by a radiating electromagnetic dipole using second-order perturbation theory in Minkowski space.

Findings

Derived the gravitational field from a radiating electromagnetic dipole.

Identified angular momentum flux in the conservation law.

Calculated the full metric perturbation in this context.

Abstract

We begin with the time-dependent electric and magnetic dipole solution of Maxwell's equations in Minkowski space. This Maxwell field is then used to determine the behavior of the gravitational field (the Weyl tensor) as a second-order perturbation off of the Minkowski background. From the Weyl tensor we go on and find the spin-coefficients and the full metric in this approximation. The physical meaning of many of the relations is discussed. In particular we can identify the conservation law of angular momentum that contains an angular momentum flux term.