[@Rezzolla:2011], is the confirmation that a magnetic-jet structure is formed in the low-density funnel produced by the black hole–torus system. Both in RMHD and in IMHD, the magnetic field is predominantly toroidal in the highly conducting torus and predominantly poloidal in the nearly evacuated funnel. Furthermore, because of the effective decoupling between the matter and the electromagnetic fields achieved in the RMHD simulations, the magnetic-jet structure is coherent on the largest scale of our system. However, as in the IMHD case, also in these RMHD simulations, the magnetic-jet structure does not lead to an ultrarelativistic outflow. Reconnection processes or neutrino annihilation occurring in the funnel could potentially increase the internal energy in the funnel and launch a relativistic outflow; none of these effects is modeled in our simulations.

The plan of the paper is as follows. In Sec. \[sec:binaries:approach\] we briefly review the mathematical setup of our simulations, concentrating mostly on the discussion of the general-relativistic RMHD equations used and on the expression of the generalized Ohm’s law we have employed. Section \[sec:numsetup\], on the other hand, is dedicated to illustrate the numerical strategy employed in the solution of the combined set of the Einstein and RMHD equations, including the 