  Neutron star mergers are among the most promising sources of gravitational
waves for advanced ground-based detectors. These mergers are also expected to
power bright electromagnetic signals, in the form of short gamma-ray bursts,
infrared/optical transients, and radio emission. Simulations of these mergers
with fully general relativistic codes are critical to understand the merger and
post-merger gravitational wave signals and their neutrinos and electromagnetic
counterparts. In this paper, we employ the SpEC code to simulate the merger of
low-mass neutron star binaries (two $1.2M_\odot$ neutron stars) for a set of
three nuclear-theory based, finite temperature equations of state. We show that
the frequency peaks of the post-merger gravitational wave signal are in good
agreement with predictions obtained from simulations using a simpler treatment
of gravity. We find, however, that only the fundamental mode of the remnant is
excited for long periods of time: emission at the secondary peaks is damped on
a millisecond timescale in the simulated binaries. For such low-mass systems,
the remnant is a massive neutron star which, depending on the equation of
state, is either permanently stable or long-lived. We observe strong
excitations of l=2, m=2 modes, both in the massive neutron star and in the form
of hot, shocked tidal arms in the surrounding accretion torus. We estimate the
neutrino emission of the remnant using a neutrino leakage scheme and, in one
case, compare these results with a gray two-moment neutrino transport scheme.
We confirm the complex geometry of the neutrino emission, also observed in
previous simulations with neutrino leakage, and show explicitly the presence of
important differences in the neutrino luminosity, disk composition, and outflow
properties between the neutrino leakage and transport schemes.
