Choptuik's critical spacetime exists

TL;DR

This paper rigorously proves the existence of a real analytic, self-similar solution in gravitational collapse, confirming Choptuik's numerical findings with a computer-assisted mathematical proof.

Contribution

It provides the first rigorous proof of Choptuik's critical spacetime solution, including explicit construction and computer-assisted validation.

Findings

Existence of a real analytic solution confirmed

Solution matches Choptuik's observed self-similarity

Proof includes explicit approximate solution and rigorous error bounds

Abstract

About twenty years ago, Choptuik studied numerically the gravitational collapse (Einstein field equations) of a massless scalar field in spherical symmetry, and found strong evidence for a universal, self-similar solution at the threshold of black hole formation. We prove rigorously the existence of a real analytic solution, that we interpret as the solution observed by Choptuik. Our construction covers an open neighborhood of the past light cone of the singularity. The proof is computer assisted. Starting from an explicit approximate solution, we show that nearby there is a true solution. The source code and a high precision data file (about 80 significant decimal digits, with rigorous error bounds) are included. We do not study perturbations.