Magnetic Surfaces in Stationary Axisymmetric General Relativity

TL;DR

This paper introduces a new method for constructing electromagnetic surface sources in stationary axisymmetric spacetimes, generalizing classical potential theory to handle discontinuous Ernst potentials, with applications to Kerr-Newman models.

Contribution

A novel formalism for deriving electromagnetic surface sources from discontinuous Ernst potentials in stationary axisymmetric spacetimes.

Findings

Derived models of surface densities for Kerr-Newman spacetime

Generalized potential theory to include discontinuous potentials

Provided a method to construct magnetic dipole sources

Abstract

In this paper a new method is derived for constructing electromagnetic surface sources for stationary axisymmetric electrovac spacetimes endowed with non-smooth or even discontinuous Ernst potentials. This can be viewed as a generalization of some classical potential theory results, since lack of continuity of the potential is related to dipole density and lack of smoothness, to monopole density. In particular this approach is useful for constructing the dipole source for the magnetic field. This formalism involves solving a linear elliptic differential equation with boundary conditions at infinity. As an example, two different models of surface densities for the Kerr-Newman electrovac spacetime are derived.