Complementary to this phenomenological approach, the next three sections contain a systematic discussion. Section 3 describes the basic mechanism of critical collapse. Key concepts are borrowed from dynamical systems and renormalization group theory. I introduce the relativistic notions of scale-invariance and scale-periodicity, define the concept of a critical solution, and sketch the calculation of the critical exponent. The following Section 4 contains both horizontal and vertical extensions to the basic picture that are, in my mind, less central. The dividing line between this and the previous section is therefore somewhat arbitrary. Section 5 groups together areas of current research where results are still lacking or tentative.

The present paper is a revised and updated version of [76]. The number of papers dedicated to critical collapse since the work of Choptuik is now more than one hundred, although not all are cited here. Previous review papers include [89, 11, 72, 21]. Choptuik's own review article is [39]. For an interesting general review of the physics of scale-invariance, see [122].

Critical Phenomena in Gravitational Collapse
Carsten Gundlach
http://www.livingreviews.org/lrr-1999-4
© Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |