Becker, Peter AKroon, John2016-09-282016-09-282016https://hdl.handle.net/1920/10462The Universe is host to a wide variety of high-energy processes that convert gravitational potential energy or rest-mass energy into non-thermal radiation such as bremsstrahlung and synchrotron. Prevailing models of X-ray emission from accreting Black Hole Binaries (BHBs) struggle to simultaneously fit the quiescent X-ray spectrum and the transients which result in the phenomenon known as X-ray time lags. And similarly, classical models of diffusive shock acceleration in pulsar wind nebulae fail to explain the extreme particle acceleration in very short timescales as is inferred from recent γ-ray flares from the Crab nebula. In this dissertation, I develop new exact analytic models to shed light on these intriguing processes.197 pagesenCopyright 2016 John KroonAstrophysicsPhysicsAstrophysicsBlack HolesCrab NebulaGamma-raysHigh-EnergyX-raysDissertation