The General Theory of Relativity discovered by Einstein tells us that the familiar, everyday force of gravity is a manifestation of something much stranger: the bending of the geometry of space-time by matter. Many of the most dramatic of observed astrophysical phenomena, seen through the windows of electromagnetic radiation or gravitational effects, occur in regions of strong gravitational and/or electromagnetic fields. Phenomena like relativistic jets outpouring from centers of galaxies or those marking the death of a massive star in a supernova explosion are examples of scenarios that can only be explained by carefully describing gravity and electromagnetic fields simultaneously. The magnetic field of the neutron star that results from a supernova explosion can be a billion times stronger than the strongest human-made magnets. Its gravitational field can be so strong that a spoonful of matter at the neutron star surface can weigh as much as a mountain on Earth. This award supports research on the strong-field environments of neutron stars and black holes, objects for which these strong-field phenomena are especially prominent. The specific systems to be studied are point masses orbiting black holes and magnetically dominated (force-free) plasmas near stars and black holes. The techniques are mainly analytical as opposed to numerical. Self-force effects on a point mass orbiting near a rapidly spinning black hole will be computed and used to inform astrophysical source modeling as well as thought experiments testing the cosmic censorship conjecture. Equations for the self-force will be formulated in alternative gauges and alternative gravitational theories. New force-free solutions will be found by exploiting spacetime methods and developing new perturbative techniques, with an overall goal of developing a broad understanding of force-free electrodynamics and its application to electromagnetic energy extraction from astrophysical black holes. The project will contribute to the training of Ph.D. students, and the research results will be disseminated to the public through research publications as well as news articles and public lectures where appropriate.