  We perform the first 3D ab-initio general-relativistic neutrino-radiation
hydrodynamics of a long-lived neutron star merger remnant spanning a fraction
of its cooling time scale. We find that neutrino cooling becomes the dominant
energy loss mechanism after the gravitational-wave dominated phase (${\sim}20\
{\rm ms}$ postmerger). Electron flavor anti-neutrino luminosity dominates over
electron flavor neutrino luminosity at early times, resulting in a secular
increase of the electron fraction in the outer layers of the remnant. However,
the two luminosities become comparable ${\sim}20{-}40\ {\rm ms}$ postmerger. A
dense gas of electron anti-neutrinos is formed in the outer core of the remnant
at densities ${\sim}10^{14.5}\ {\rm g}\ {\rm cm}^{-3}$, corresponding to
temperature hot spots. The neutrinos account for ${\sim}10\%$ of the lepton
number in this region. Despite the negative radial temperature gradient, the
radial entropy gradient remains positive and the remnant is stably stratified
according to the Ledoux criterion for convection. A massive accretion disk is
formed from the material squeezed out of the collisional interface between the
stars. The disk carries a large fraction of the angular momentum of the system,
allowing the remnant massive neutron star to settle to a quasi-steady
equilibrium within the region of possible stable rigidly rotating
configurations. The remnant is differentially rotating, but it is stable
against the magnetorotational instability. Other MHD mechanisms operating on
longer timescales are likely responsible for the removal of the differential
rotation. Our results indicate the remnant massive neutron star is thus
qualitatively different from a protoneutron stars formed in core-collapse
supernovae.
