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

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.

33 pages, 21 figures; V2 updated to match published version

References in corpus (16)

• Three-dimensional numerical simulations of the pulsar magentoshere: Preliminary results
• "Meissner effect" and Blandford-Znajek mechanism in conductive black hole magnetospheres
• General Relativistic Force-Free Electrodynamics: A New Code and Applications to Black Hole Magnetospheres
• 3D Relativistic Magnetohydrodynamic Simulations of Magnetized Spine-Sheath Relativistic Jets
• Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations
• Accurate Simulations of Binary Black-Hole Mergers in Force-Free Electrodynamics
• Testing outer boundary treatments for the Einstein equations
• Electromagnetic power of merging and collapsing compact objects
• Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity
• Force-Free Electrodynamics around Extreme Kerr Black Holes
• Stability of Force-Free Magnetospheres
• Magnetosphere of a Kerr black hole immersed in magnetized plasma and its perturbative mode structure
• On the Linear Stability of Magnetized Jets Without Current Sheets: Non-Relativistic Case
• A geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad
• Force-free magnetosphere of an aligned rotator with differential rotation of open magnetic field lines
• Pulsar electrodynamics: a time-dependent view

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• Particle acceleration driven by null electromagnetic fields near a Kerr black hole