Low angular momentum general relativistic magnetohydrodynamic accretion flow around rotating black holes with shocks

We investigate the global structure of general relativistic magneto-hydrodynamic (GRMHD) accretion flows around Kerr black holes containing shock waves, where the disk is threaded by radial and toroidal magnetic fields. We self-consistently solve the GRMHD equations that govern the flow motion inside the disk and for the first time to our knowledge, we obtain the shock-induced global GRMHD accretion solutions around weakly as well as rapidly rotating black holes for a set of fundamental flow parameters, such as energy ($E$), angular momentum ($L$), radial magnetic flux ($\Phi$), and iso-rotation parameter ($F$). We show that shock properties, namely shock radius ($r_{\rm sh}$), compression ratio ($R$) and shock strength ($\Psi$) strongly depends on $E$, $L$, $\Phi$, and $F$. We observe that shock in GRMHD flow continues to exist for wide range of the flow parameters, which allows us to identify the effective domain of parameter space in $L-E$ plane where shock solutions are feasible. Moreover, we examine the modification of the shock parameter space and find that it shifts towards the lower angular momentum values with increasing $\Phi$ and black hole spin ($a_{\rm k}$). Finally, we compute the critical radial magnetic flux ($\Phi^{\rm cri}$) that admits shocks in GRMHD flow and ascertain that $\Phi^{\rm cri}$ is higher (lower) for black hole of spin $a_{\rm k} = 0.99$ ($0.0$) and vice versa.