Critical Phenomena in Gravitational Collapse

It was well known that strong enough initial configurations of matter field would result in gravitational collapse to black holes, whereas weak enough initial data become dispersed to infinity. However, what happens in the intermediate region was not clear until the discovery of the critical phenomena in gravitational collapse by Choptuik in 1993 [1]. He examined numerically the spacetime evolution of massless scalar field minimally coupled to gravitational field. The model studied is the simplest one so that numerical studies are practical and accurate enough. His discovery is remarkable. There’s three major phenomena. The first is the mass scaling law in the resulting black hole mass M :