properties of our computational grid, of our matching to the low-density exterior, and of our initial data. The core of the paper is represented by Sec. \[sec:binaries:results\], where we present our results. After a brief overview, we discuss the magnetic-field topology and magnetic-jet structure produced in the simulations, as well as the comparison with the IMHD case. Such a comparison goes over a number of aspects, from the angular-momentum transfer and lifetime of the HMNS, over to the black hole–torus system, and the electromagnetic luminosities. Finally, Sec. \[sec:binaries:conclusions\] contains a conclusive summary of our results and the prospects for future research. Although this is not the focus of this work, an illustration of the magnetic-jet structure obtained in the IMHD simulations is presented in Appendix \[sec:appendix:imhd\] for completeness.

We use a spacelike signature $(-,+,+,+)$ and a system of units in which $c=G={M_{\odot}}=1$ unless stated differently.

Mathematical Setup {#sec:binaries:approach}
==================

General-relativistic RMHD equations {#sec:ms:rmhd}
-----------------------------------

Much of the numerical setup used in these simulations has been presented in greater detail in other papers [@Giacomazzo:2007ti; @Baiotti08; @Baiotti:2009gk; @Giacomazzo:2009mp; @Baiotti:2010ka; @Dionysopoulou:2012pp], and for compactness we will review here only the basic aspects, referring the interested reader to the papers above for additional information. 