Chairperson, Graduate Committee: Yves U. IdzerdaThoelecke, Kevin2019-10-212019-10-212019https://scholarworks.montana.edu/handle/1/15605Spinning black holes can store enormous amounts of rotational energy. Efficiently extracting that rotational energy can lead to significant energy outflows capable of powering very high energy astrophysical phenomena, such as gamma-ray bursts and active galactic nuclei. Black holes are unique in that they do not exist as physical objects in the same way a rock, planet, or star exists; instead, black holes exist only as spacetime curvature. As such processes for extracting a black hole's rotational energy are largely unique to black holes. This work explores one such process, the extraction of a black hole's rotational energy via an appropriately configured magnetosphere. Both analytic perturbation techniques and numerical codes are developed in order to solve for thousands of energy-extracting black hole magnetospheres. Those magnetospheres broadly sample the relevant solution space, allowing correlations to be drawn between different rates of black hole rotational energy and angular momentum extraction and global magnetosphere structure. The most fundamental behavior discovered is that magnetospheres that extract the most energy per unit angular momentum direct that energy away from the black hole's rotational axis, while magnetospheres that extract the least amount of energy per unit angular momentum direct that energy into jet-like structures aligned with the black hole's rotational axis. Exploration of the solutions obtained also suggests that magnetospheres most compatible with nearby accreting matter can very naturally launch jets, implying that black hole energy extraction and jet launching are likely to be concurrent and common features of astrophysical black hole magnetospheres.enBlack holes (Astronomy)Rotational motionMagnetohydrodynamicsAstrophysicsDissertationCopyright 2019 by Kevin Thoelecke