  We describe the current status of our numerical simulations for the collapse
of a massive stellar core to a BH and the BNS mergers, performed in the
framework of full general relativity incorporating finite-temperature EOS and
neutrino cooling. For the stellar core collapse simulation, we present the
latest numerical results. We employed a purely nucleonic EOS (Shen-EOS). As an
initial condition, we adopted a 100 $M_{\odot}$ presupernova model calculated
by Umeda and Nomoto. Changing the degree of rotation for the initial condition,
we clarify the strong dependence of the outcome of the collapse on this. When
the rotation is rapid enough, the shock wave formed at the core bounce is
deformed to be a torus-like shape. Then, the infalling matter is accumulated in
the central region due to the oblique shock at the torus surface, hitting the
PNS and dissipating the kinetic energy there. As a result, outflows can be
launched. The PNS eventually collapses to a BH and an accretion torus is formed
around it. We also found that the evolution of the BH and torus depends
strongly on the rotation initially given. In the BNS merger simulations, we in
addition employ an EOS incorporating a degree of freedom for hyperons. The
numerical simulations show that for the purely nucleonic EOS, a HMNS with a
long lifetime ($\gg 10$ ms) is the outcome for the total mass $M \lesssim
3.0M_{\odot}$. By contrast, the formed HMNS collapses to a BH in a shorter time
scale with the hyperonic EOS for $M \gtrsim 2.7M_{\odot}$. It is shown that the
typical total neutrino luminosity of the HMNS is $\sim 3$--$10\times 10^{53}$
ergs/s and the effective amplitude of gravitational waves from the HMNS is
2--$6 \times 10^{-22}$ at $f\approx 2$--2.5 kHz for a source distance of 100
Mpc.
