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 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.

Novel scheme for simulating the force-free equations: Boundary conditions and the evolution of solutions towards stationarity

“…Considerable analytical and numerical efforts have concentrated on the study of black hole magnetospheres under the force-free approximation (see e.g. [7,[16][17][18][19][20][21][22][23][24][25][26][27][28]). Numerical simulations started to look at more realistic astrophysical scenarios beyond the monopole, splitmonopole and paraboloidal field configurations of the original BZ work.…”

Particle Acceleration Driven by Null Electromagnetic Fields Near a Kerr Black Hole

“…This mimics some physical mechanisms of electromagnetic energy loss; the energy is locally dissipated. Some part of the energy is also carried away by a burst wave, which may be approximated by a null field, as suggested by the perturbation analysis of FFE [25][26][27]. Thus, we expect that the null FFE field or the field approximated by it must appear as a burst near a black hole and propagate outwardly.…”

“…Such an electromagnetic field propagates at the speed of light, and the four-current is a null vector. The field is analogous to the traveling-wave mode that appears in the dynamical perturbations of stationary force-free solutions [25][26][27]. The wave propagates along the principal null direction of the background spacetime without any back scattering.…”

Crystals of gauged solitons, force free plasma and resurgence

“…In recent years relevant analytic examples of FFP have been constructed (see, for instance, [14], [15], [16], [17], [18], [19], [20], [21], [22], [23] and references therein), however, many of the available examples (which analyze in detail solutions of the system in Eq. ( 1)) leave open the issue to identify the actual sources of the force-free electromagnetic field.…”