http://arxiv.org/abs/1501.05394
Recently, a family of exact force-free electrodynamic (FFE) solutions was discovered by Brennan, Gralla and Jacobson, which generalizes earlier solutions by Menon and Dermer, Michel, 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 possesses 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 pseudo-spectral 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.
F. Zhang, S. McWilliams and H. Pfeiffer
Fri, 23 Jan 15
49/65
Comments: 24 pages, 14 figures
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