Aspects of classical and quantum black holes

There are many gravity theories that contain black holes as their classical solutions. Large class of effectively 2-dimensional gravity theories continuously connecting the CGHS model, inspired by string theory, and the spherically symmetric reduction of d-dimensional Einstein gravity theory are such examples. For these theories, we establish Birkhoff's theorem and the no-scalar-hair theorem, which were the major properties of phenomenologically important spherically symmetric 4-d Einstein gravity. This connection suggests some of the lessons from one theory may be useful in tackling the similar but more difficult problems in the other theory.; Two such problems, the classical black hole formation and the quantum gravitational corrections to the Hawking radiation from black holes, are then considered. Via numerical analysis, the dynamical formation of black holes after the classical gravitational collapse in s-wave Einstein gravity has been known for some time to show a critical behavior, a second order phase transition. We demonstrate the same story analytically and consider the similar phenomena in other gravity theories.; Then, we study the Hawking radiation process in 4-d Einstein gravity. The quantum gravitational corrections, via the gravitational scattering between the in-falling matter and the outgoing Hawking radiation, are shown to have a significant effect on the calculation of final states. In particular, as seen by an outside observer, they produce a fast growing uncertainty in the position of the in-falling matter as it approaches the black hole horizon. These considerations lead to a possible realization of the black hole complementary principle, which provides some insight toward the understanding of the information paradox in the Hawking radiation.