  Merging binary neutron stars (BNSs) represent the ultimate targets for
multimessenger astronomy, being among the most promising sources of
gravitational waves (GWs), and, at the same time, likely accompanied by a
variety of electromagnetic counterparts across the entire spectrum, possibly
including short gamma-ray bursts (SGRBs) and kilonova/macronova transients.
Numerical relativity simulations play a central role in the study of these
events. In particular, given the importance of magnetic fields, various aspects
of this investigation require general relativistic magnetohydrodynamics
(GRMHD). So far, most GRMHD simulations focused the attention on BNS mergers
leading to the formation of a hypermassive NS, which, in turn, collapses within
few tens of ms into a black hole surrounded by an accretion disk. However,
recent observations suggest that a significant fraction of these systems could
form a long-lived NS remnant, which will either collapse on much longer
timescales or remain indefinitely stable. Despite the profound implications for
the evolution and the emission properties of the system, a detailed
investigation of this alternative evolution channel is still missing. Here, we
follow this direction and present a first detailed GRMHD study of BNS mergers
forming a long-lived NS. We consider magnetized binaries with different mass
ratios and equations of state and analyze the structure of the NS remnants, the
rotation profiles, the accretion disks, the evolution and amplification of
magnetic fields, and the ejection of matter. Moreover, we discuss the
connection with the central engine of SGRBs and provide order-of-magnitude
estimates for the kilonova/macronova signal. Finally, we study the GW emission,
with particular attention to the post-merger phase.
