  We present the first results from our new general relativistic, Lagrangian
hydrodynamics code, which treats gravity in the conformally flat (CF) limit.
The evolution of fluid configurations is described using smoothed particle
hydrodynamics (SPH), and the elliptic field equations of the CF formalism are
solved using spectral methodsin spherical coordinates. The code was tested on
models for which the CF limit is exact, finding good agreement with the
classical Oppenheimer-Volkov solution for a relativistic static spherical star
as well as the exact semi-analytic solution for a collapsing spherical dust
cloud. By computing the evolution of quasi-equilibrium neutron star binary
configurations in the absence of gravitational radiation backreaction, we have
confirmed that these configurations can remain dynamically stable all the way
to the development of a cusp. With an approximate treatment of radiation
reaction, we have calculated the complete merger of an irrotational binary
configuration from the innermost point on an equilibrium sequence through
merger and remnant formation and ringdown, finding good agreement withprevious
relativistic calculations. In particular, we find that mass loss is highly
suppressed by relativistic effects, but that, for a reasonably stiff neutron
star equation of state, the remnant is initially stable against gravitational
collapse because of its strong differential rotation. The gravity wave signal
derived from our numerical calculation has an energy spectrum which matches
extremely well with estimates based solely on quasi-equilibrium results,
deviating from the Newtonian power-law form at frequencies below 1 kHz, i.e.,
within the reach of advanced interferometric detectors.
