Coulomb fields as perturbations of type D vacuum space-times

TL;DR

This paper demonstrates that a specific Coulomb-like electromagnetic field can exist as a solution on type D vacuum spacetimes without perturbing their mass or angular momentum, highlighting its non-influence on the background geometry.

Contribution

It introduces a special non-null electromagnetic field solution aligned with principal null directions on type D backgrounds, showing it does not affect the spacetime's mass or angular momentum.

Findings

The Coulomb field behaves as 1/r^2.

The energy and angular momentum fluxes vanish for this field.

The field does not perturb the parameters of Kerr, Kerr-Taub-NUT, Taub-NUT, or Schwarzschild spacetimes.

Abstract

We consider a test, non-null electromagnetic field special in the sense that the principal null directions of the field lie along the two repeated principal null directions of the type D vacuum background. We prove that the special non-null field is a valid solution of the Maxwell equations on a type D background. This field behaves as $1/r^2$ and the only non-vanishing Maxwell scalar is $\phi_1$ so it can be called the Coulomb field. We show that the contribution to the energy and angular momentum fluxes of the Coulomb field vanishes at any surface of integration, on the type D vacuum backgrounds Kerr, Kerr-Taub-NUT, Taub-NUT, and Schwarzschild. Therefore this field does not lead to any perturbations of the mass and angular momentum parameters of these space-times.