A mechanism for black hole formation where the mass depends sensitively on initial conditions near a threshold.Critical collapse is a mechanism for black hole formation that occurs when a collapsing wave of matter (such as a scalar field or gravitational waves) is tuned precisely to a threshold. At this critical point, the mass of the resulting black hole depends sensitively on the initial conditions, following a power-law scaling: the mass is proportional to (p - p*)^γ, where p is a parameter like the amplitude of the initial pulse, p* is the critical value, and γ is a universal exponent. This behavior is analogous to phase transitions in statistical mechanics, where systems exhibit critical phenomena near a phase boundary.
Critical collapse was discovered in 1993 by Matthew Choptuik, who found it through numerical simulations of a massless scalar field collapsing in general relativity. His work revealed the universal scaling and self-similarity, which was a surprise and sparked extensive theoretical and numerical research.
When a collapsing configuration is slightly above the critical threshold, it forms a black hole with a tiny mass, while slightly below, it disperses entirely. Near the threshold, the dynamics become self-similar: the collapsing matter repeats a pattern on ever-smaller scales, leading to a 'critical solution' that is universal—independent of the initial shape of the wave. The black hole mass scales as a power law with the distance from criticality, and the exponent γ depends on the type of matter but is the same for all initial conditions of that type. This arises from the nonlinearity of Einstein's equations, which amplify tiny differences in initial data near the threshold.
Critical collapse is primarily a theoretical tool for understanding black hole formation and the nonlinear dynamics of general relativity, but it also informs numerical relativity codes used to simulate gravitational wave sources like binary black hole mergers.
The critical exponent γ for a massless scalar field is approximately 0.37, and it is the same for any initial shape of the wave, a universality that mirrors critical exponents in condensed matter physics.














