  A differentially rotating hypermassive neutron star (HMNS) is a metastable
object which can be formed in the merger of neutron-star binaries. The eventual
collapse of the HMNS into a black hole is a key element in generating the
physical conditions expected to accompany the launch of a short gamma-ray
burst. We investigate the influence of magnetic fields on HMNSs by performing
three-dimensional simulations in general-relativistic magnetohydrodynamics. In
particular, we provide direct evidence for the occurrence of the
magnetorotational instability (MRI) in HMNS interiors. For the first time in
simulations of these systems, rapidly-growing and spatially-periodic structures
are observed to form with features like those of the channel flows produced by
the MRI in other systems. Moreover, the growth time and wavelength of the
fastest-growing mode are extracted and compared successfully with analytical
predictions. The MRI emerges as an important mechanism to amplify magnetic
fields over the lifetime of the HMNS, whose collapse to a black hole is
accelerated. The evidence provided here that the MRI can actually develop in
HMNSs could have a profound impact on the outcome of the merger of neutron-star
binaries and on its connection to short gamma-ray bursts.
