  We performed 3D numerical simulations of the merger of equal-mass binary
neutron stars in full general relativity using a new large scale supercomputer.
We take the typical grid size as (505,505,253) for (x,y,z) and the maximum grid
size as (633,633,317). These grid numbers enable us to put the outer boundaries
of the computational domain near the local wave zone and hence to calculate
gravitational waveforms of good accuracy (within $\sim 10%$ error) for the
first time. To model neutron stars, we adopt a $\Gamma$-law equation of state
in the form $P=(\Gamma-1)\rho\epsilon$, where P, $\rho$, $\varep$ and $\Gamma$
are the pressure, rest mass density, specific internal energy, and adiabatic
constant. It is found that gravitational waves in the merger stage have
characteristic features that reflect the formed objects. In the case that a
massive, transient neutron star is formed, its quasi-periodic oscillations are
excited for a long duration, and this property is reflected clearly by the
quasi-periodic nature of waveforms and the energy luminosity. In the case of
black hole formation, the waveform and energy luminosity are likely damped
after a short merger stage. However, a quasi-periodic oscillation can still be
seen for a certain duration, because an oscillating transient massive object is
formed during the merger. This duration depends strongly on the initial
compactness of neutron stars and is reflected in the Fourier spectrum of
gravitational waves. To confirm our results and to calibrate the accuracy of
gravitational waveforms, we carried out a wide variety of test simulations,
changing the resolution and size of the computational domain.

General Relativity and Quantum Cosmology