Critical Phenomena in Gravitational Collapse: The Studies So Far

Studies of black hole formation from gravitational collapse have revealed interesting non-linear phenomena at the threshold of black hole formation. In particular, in 1993 Choptuik studied the collapse of a massless scalar field with spherical symmetry and found some behaviour, which is quite similar to the critical phenomena well-known in {\em Statistical Mechanics} and {\em Quantum Field Theory}. Universality and echoing of the critical solution and power-law scaling of the black hole masses have given rise to the name {\em Critical Phenomena in Gravitational Collapse}. Choptuik's results were soon confirmed both numerically and semi-analytically, and have extended to various other matter fields. In this paper, we shall give a brief introduction to this fascinating and relatively new area, and provides an updated publication list. An analytical "toy" model of critical collapse is presented, and some current investigations are given.Comment: 5 figures, revtex. To appear in Braz. J. Phys. (2001

On Gauge Choice of Spherically Symmetric 3-Branes

Gauge choice for a spherically symmetric 3-brane embedded in a D-dimensional bulk with arbitrary matter fields on and off the brane is studied. It is shown that Israel's junction conditions across the brane restrict severely the dependence of the matter fields on the spacetime coordinates. As examples, a scalar field or a Yang-Mills potential can be only either time-dependent or radial-coordinate dependent for the chosen gauge, while for a perfect fluid it must be co-moving.Comment: Latex, final version to appear in Class. Quantum Gra