Dynamics in the Magnetospheres of Compact Objects

This Ph.D. thesis explores the modeling of dynamics in magnetospheres around compact objects (black holes and neutron stars), and their implications in the formation of high energy phenomena such as magnetar flares and the highly variable teraelectron Volt (TeV) emission of some active galactic nuclei, by means of numerical simulations. The amazing images of black hole (BH) shadows from the galactic center and the M87 galaxy provide a first direct glimpse into the physics of accretion flows in the most extreme environments of the universe. The efficient extraction of energy in the form of collimated outflows or jets from a rotating BH is directly linked to the topology of the surrounding magnetic field. General Relativistic force-free electrodynamics (GRFFE) is one possible plasma limit employed to analyze energetic outflows in which strong magnetic fields are dominant over all inertial phenomena. In this work, we present numerical strategies capable of modeling both, stationary, and fully dynamic force-free magnetospheres of compact objects. The latter is provided by an implementation of GRFFE on the infrastructure of the Einstein Toolkit. This Ph.D. thesis reviews the methodology behind this newly developed code package and its application to magnetars and rapidly spinning BHs in detail. Scientific results of this project are presented by a series of publications. We improved the numerical techniques used to solve for equilibrium magnetospheres of Kerr BHs across their singular surfaces and provide a first detailed review of convergence properties. Furthermore, we identified instabilities in the high energy branches of twisted magnetar magnetospheres which may act as the triggering mechanism of the most powerful soft-gamma repeaters (SGRs). Finally, we confirmed the possibility of energy extraction by the Blandford/Znajek mechanism from rapidly spinning BHs in 3D dynamical magnetospheres induced by the accretion of small scale magnetic structures.