Black holes as the central engines for astrophysical sources

The extraction of gravitational potential energy from matter which accretes into the deep potential well of black holes is believed to be the central engine of several important energetic sources in the Universe, such as active galactic nucleus (AGNs), gamma ray bursts (GRBs), X-ray binaries (XRBs), and so on. In this talk, I give a brief review of our recent works on black hole astrophysics. These works include: the possible observational properties of the afterglow of ultra-luminous quasars; the observed profile of an emission line from the conical jets around rotating a black hole; the temporal evolution of the hyperaccretion flow under beta equilibrium; and the relationship between the lack of type I x-ray bursts in XRBs and the evidence for black hole event horizons.