General Relativistic Magnetohydrodynamics (GRMHD)
and Formation of Black Hole Relativistic Jet
General relativistic magnetohydrodynamic (GRMHD) flows along magnetic fields threading a black hole can be divided into inflow and outflow parts, according to the result of the competition between the black hole gravity and magneto-centrifugal forces along the field line.
Assuming black hole jet is powered by black hole rotation, the necessary condition for black hole jet formation is to extract the black hole rotational energy successfully, which can only be realized when the GRMHD inflow is magnetically dominated (see here for a summary of black hole jet formation).
It is straightforward to discuss the BH disk-jet coupling according to how different types of accretion flow (see here for a summary of black hole accretion flow) can affect magnetically dominance of the GRMHD flow along the hole-threading field lines, and therefore the jet launching and quenching.
Furthermore, once the black hole energy is extracted outward,the outflow part of the solution can be constrained by the inflow part, by assuming that the dominating (electromagnetic) component of the energy flux per flux tube is conserved at the surface where the inflow and outflow are separated.