We focus on case studies involving magnetic configurations in the Sun and stellar, gas dynamics, Hamiltonian mechanics, and electrodynamics around black holes. The predictions aim to make new advances in understanding various phenomena like magnetic topology and flare mechanisms, tidal disruption events around massive black holes, and their observational appearance. This is a proposal projecting theoretical physics problems in MHD and relativity whose results can be tested by simulations and also provide explanations to observations from current and future observations from various ground and space-based telescopes that India is currently participating in, such as ADITYA (studying solar atmosphere problems), ASTROSAT (to probe oscillations in high energy emission from gas around black holes), TMT (to probe stellar dynamics around black holes), and LIGO (gravitational wave detection from black holes). With the foundations already made, the following problems are now being worked on both in the short term and long-term: 1. Star cluster dynamics around Binary black holes, its evolution to in-spirals, and implication for gravitational wave detection and demographics 2. Modeling black hole demographics based on the model presented 3. Free energy estimates for multibraid systems to make predictions for energy distribution of nanoflares for heating in by the quiet Sun. 4. Using null geodesic solutions from Hamiltonian mechanics derived in a new coordinate system, we plan to apply it to black hole imaging and light echoes as a possible origin for QPOs in BHXRBs. 5. Study of wave propagation in twisted flux tubes using perturbation theory. 6. Stability of spherical stellar systems.