Regular Rotating Black Hole: Probing the boundaries of the Radiative Signatures and Jet Power

We perform a detailed observational analysis of several galactic X-ray binaries, focusing on the interplay between black hole spin, jet power, and radiative efficiency within the context of Blandford-Znajek-powered jets. Using updated measurements from continuum fitting and Fe-line methods, we constrain the spin parameter a and the deviation parameter $β$ for five key black hole systems: H1743-322, XTE J1550-564, GRS 1124-683, GRO J1655-40, and GRS 1915+105. For each system, we compare the allowed parameter spaces derived independently from observed radiative efficiencies and emitted jet powers under different assumptions for the jet Lorentz factor $Γ=2,5$. By overlapping these observational constraints with theoretical expectations for regular black holes, we assess the viability of various spin-deviation combinations in explaining the observed phenomena. Our results reveal significant restrictions on the allowed values of $β$, with typical upper bounds around 0.38 - 0.4, except for rapidly spinning sources where the constraint becomes notably tighter. We further present a modified method for generating rotating solutions from static regular black hole spacetimes and provide a robust theoretical framework for relating jet power to black hole angular frequency in curved geometries. We also find that the theoretical jet power is modified by regularization factor for regular black holes. These findings place stringent observational bounds on deviations from the Kerr geometry and provide important insight into the astrophysical mechanisms powering accreting stellar-mass black holes.