Gravitational interactions and energetic phenomena in stellar systems around stellar-mass black holes

Stellar-mass black hole binaries represent critical environments for exploring the complex coupling between relativistic gravity, angular momentum transport, and high-energy radiation. This work investigates how black hole spin and orbital separation modulate mass transfer efficiency, jet energetics, and emission behaviour in such systems. To this end, we employ a hybrid framework combining analytical models with two-dimensional general relativistic magnetohydrodynamics (GRMHD) simulations, focusing on variations in gravitational potential, inflow rate, and spectral structure across a range of black hole masses (M) and spin values (a). We introduce a novel empirical formulation for the mass transfer rate, M(r,M͙, a), which captures non-linear spin-radius coupling and enables accurate modelling of disk-jet interaction. Our simulations reveal that a critical spin threshold around a ≈ 0.7 leads to a steep rise in jet power, in alignment with Blandford–Znajek predictions. Furthermore, relativistically redshifted emission spectra derived from disk regions show strong agreement with observed X-ray data from Cygnus X-1 and V404 Cygni. These results establish a predictive link between system configuration and observable features, offering a robust foundation for interpreting spectral and timing behaviour in accreting black hole binaries.