The Choptuik spacetime as an eigenvalue problem

TL;DR

This paper formulates the critical spacetime in scalar field collapse as an eigenvalue problem, solving numerically for the rescaling factor that characterizes the phase transition between black hole formation and dispersion.

Contribution

It introduces a novel eigenvalue approach to determine the critical spacetime in scalar field collapse, providing a precise numerical value for the scaling factor.

Findings

Eigenvalue for the rescaling factor Delta = 3.4439 +/- 0.0004

Critical spacetime characterized by discrete scale-invariance and symmetry conditions

Numerical solution of a nonlinear hyperbolic boundary value problem

Abstract

By fine-tuning generic Cauchy data, critical phenomena have recently been discovered in the black hole/no black hole "phase transition" of various gravitating systems. For the spherisymmetric real scalar field system, we find the "critical" spacetime separating the two phases by demanding discrete scale-invariance, analyticity, and an additional reflection-type symmetry. The resulting nonlinear hyperbolic boundary value problem, with the rescaling factor Delta as the eigenvalue, is solved numerically by relaxation. We find Delta = 3.4439 +/- 0.0004.