Ideas from dynamical systems theories provide a qualitative understanding of the time evolution of initial data near any of these boundaries. At the particular boundary between initial data that form black holes and data that disperse, scale-invariance plays an important role in the dynamics. This gives rise to a power law for the black hole mass. Scale-invariance, universality and power-law behavior suggest the name ``critical phenomena in gravitational collapse''.
Critical phenomena in statistical mechanics and in gravitational collapse share scale-invariant physics and the presence of a renormalization group, but while the former involves statistical ensembles, general relativity is deterministically described by partial differential equations (PDEs).
|Critical Phenomena in Gravitational Collapse
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