  Viscosity and magnetic fields drive differentially rotating stars toward
uniform rotation, which has important consequences in many astrophysical
contexts. For example, merging binary neutron stars can form a "hypermassive"
remnant, i.e. a differentially rotating star with a mass greater than the
maximum allowed by uniform rotation. The removal of the centrifugal support
provided by differential rotation can lead to delayed collapse of the remnant
to a black hole, accompanied by a burst of gravitational radiation. Both
magnetic fields and viscosity alter the structure of differentially rotating
stars on secular timescales, making numerical tracking of the evolution
difficult. Here, we present the first simulations of rapidly rotating stars
with shear viscosity in full general relativity. We self-consistently include
viscosity in our relativistic hydrodynamic code to solve the relativistic
Navier-Stokes equations both in axisymmetry and in full 3+1 dimensions. In
axisymmetry, we follow secular evolution with high resolution over dozens of
rotation periods (thousands of M). We find that viscosity operating in a
hypermassive star generically leads to the formation of a compact, uniformly
rotating core surrounded by a low-density disk. These uniformly rotating cores
are often, but not always, unstable to gravitational collapse. In the unstable
cases, we follow the collapse and determine the mass and the spin of the final
black hole and ambient disk. In all cases studied, the rest mass of the
resulting disk is found to be 10-20% of the original star, whether surrounding
a uniformly rotating core or a rotating black hole. This study foreshadows more
detailed, future simulations of secular processes, including magnetic effects,
in relativistic stars.
