Critical Behaviour in Scalar Field Collapse

Abstract

I present an account of the discovery of critical behaviour in spherically-symmetric general-relativistic collapse of a scalar field, φ. Using an adaptive mesh-refinement algorithm in conjunction with finite-difference techniques, I have studied the non-linear evolution of parameterized initial configurations φ(r, 0; p), where a critical parameter value, p = p*, generically demarcates the transition from spacetimes which do not contain a final black hole to spacetimes which do. The near critical regime, p ≈ p*, is characterized by a variety of non-linear phenomena including exponential sensitivity to initial conditions, scale-periodicity, and universal power-law dependence of black hole mass on parameter-space displacement |p − p*|.