Stability of exact force-free electrodynamic solutions and scattering from spacetime curvature

TL;DR

This paper demonstrates the stability of a family of exact force-free electrodynamic solutions through nonlinear simulations, introduces a new FFE code, and analyzes how spacetime curvature affects electromagnetic scattering.

Contribution

It provides the first stability analysis of these exact FFE solutions, introduces a high-accuracy FFE simulation code, and offers insights into electromagnetic scattering in curved spacetime.

Findings

The FFE solutions are stable under small perturbations.

The new pseudospectral FFE code achieves exponential convergence.

Spacetime curvature simplifies electromagnetic scattering along null directions.

Abstract

Recently, a family of exact force-free electrodynamic (FFE) solutions was given by Brennan, Gralla and Jacobson, which generalizes earlier solutions by Michel, Menon and Dermer, and other authors. These solutions have been proposed as useful models for describing the outer magnetosphere of conducting stars. As with any exact analytical solution that aspires to describe actual physical systems, it is vitally important that the solution possess the necessary stability. In this paper, we show via fully nonlinear numerical simulations that the aforementioned FFE solutions, despite being highly special in their properties, are nonetheless stable under small perturbations. Through this study, we also introduce a three-dimensional pseudospectral relativistic FFE code that achieves exponential convergence for smooth test cases, as well as two additional well-posed FFE evolution systems in the appendix that have desirable mathematical properties. Furthermore, we provide an explicit analysis that demonstrates how propagation along degenerate principal null directions of the spacetime curvature tensor simplifies scattering, thereby providing an intuitive understanding of why these exact solutions are tractable, i.e. why they are not backscattered by spacetime curvature.