Numerical Modeling of High-energy Transients from Black Holes and Neutron Stars

Along with recent breakthroughs in relativistic astrophysics and multi-messenger astronomy, theoretical studies on compact objects and the dynamics of relativistic matter surrounding them have a growing significance. General relativistic approaches are required to properly describe astrophysical phenomena taking place in a strong gravity regime, yet the high complexity and nonlinearity of the equations governing those systems compel numerical approaches. In this thesis, we develop a computational method for and present global numerical simulations of relativistic plasma around compact objects, particularly focusing on high-energy electromagnetic transients originating from black holes and neutron stars. Our works include a new hybrid numerical scheme for modeling force-free magnetospheres of compact objects, large-scale simulations of a spinning black hole immersed in a magnetized wind, and magnetospheric transients from a merging black hole--neutron star binary.