Poynting vector in stationary axisymmetric electrovacuum spacetimes reexamined

TL;DR

This paper derives an invariant formula for the Poynting vector in stationary axisymmetric electrovacuum spacetimes using the Ernst formalism, and applies it to solutions involving a charged magnetic dipole.

Contribution

It introduces a simple, duality-invariant formula for the Poynting vector within the Ernst formalism and demonstrates its application to exact solutions.

Findings

Derived an invariant formula for the Poynting vector

Applied the formula to charged magnetic dipole solutions

Enhanced understanding of electromagnetic energy flow in these spacetimes

Abstract

A simple formula, invariant under the duality rotation \Phi -> exp(i\alpha) \Phi, is obtained for the Poynting vector within the framework of the Ernst formalism, and its application to the known exact solutions for a charged massive magnetic dipole is considered.