  Three-dimensional simulations for the merger of binary neutron stars (BNSs)
are performed in the framework of full general relativity. We pay particular
attention to the black hole (BH) formation case and to the resulting mass of
the surrounding disk for exploring possibility for formation of the central
engine of short-duration gamma-ray bursts. Hybrid equations of state (EOSs) are
adopted mimicking realistic, stiff nuclear EOSs, for which the maximum allowed
gravitational mass of cold and spherical neutron stars (NSs), M_sph, is larger
than 2M_sun. For the simulations, we focus on BNSs of the ADM mass M>2.6M_sun.
For M>M_thr, the merger results in prompt formation of a BH irrespective of the
mass ratio Q_M with 0.65<Q_M<1. The value of M_thr is approximately written as
1.3-1.35M_sph for the chosen EOSs. For the BH formation case, we evolve the
spacetime using a BH excision technique and determine the mass of a
quasistationary disk surrounding the BH. The disk mass steeply increases with
decreasing the value of Q_M for given ADM mass and EOS. For M<M_thr, the
outcome is a hypermassive neutron star (HMNS) of a large ellipticity. If the
HMNS collapses to a BH after the longterm angular momentum transport, the disk
mass may be >0.01M_sun. Gravitational waves (GWs) are computed in terms of a
gauge-invariant wave extraction technique. In the formation of the HMNS,
quasiperiodic GWs of frequency (3-3.5kHz) are emitted. The effective amplitude
of GWs can be >5x10^{-21} at a distance of 50 Mpc. For the BH formation case,
the BH excision technique enables a longterm computation and extraction of
ring-down GWs associated with a BH quasinormal mode. It is found that the
frequency and amplitude are 6.5-7kHz and 10^{-22} at a distance of 50Mpc for
M=2.7-2.9M_sun.
