  The association of GRB170817A with GW170817 has confirmed the long-standing
hypothesis that binary neutron star (BNS) mergers are the progenitors of at
least some short gamma-ray bursts (SGRBs). This connection has ushered in an
era in which broadband observations of SGRBs, together with measurements of the
time delay between the gravitational waves and the electromagnetic radiation,
allow to probe the properties of the emitting outflow and its engine to an
unprecedented detail. Since the structure of the radiating outflow is molded by
the interaction of a relativistic jet with the binary ejecta, it is of
paramount importance to study the system in a realistic setting. Here we
present a three-dimensional hydrodynamic simulation of a relativistic jet
propagating in the ejecta of a BNS merger, which were computed with a general
relativistic magnetohydrodynamic simulation. We find that the jet's centroid
oscillates around the axis of the system, due to inhomogeneities encountered in
the propagation. These oscillations allow the jet to find the path of least
resistance and travel faster than an identical jet in smooth ejecta. In our
setup the breakout time is ~0.6 sec, comparable to the expected central engine
duration in SGRBs and possibly a non-negligible fraction of the total delay
between the gravitational and gamma-ray signals. Our simulation also shows that
energy is carried in roughly equal amounts by the jet and by the cocoon, and
that about 20 per cent of the injected energy is transferred to the ejecta via
mechanical work.
