Choptuik's critical spacetime exists

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.

46 pages

References in corpus (2)

• Critical phenomena in gravitational collapse
• Codimension-two critical behavior in vacuum gravitational collapse

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• Black Hole Critical Collapse in Infinite Dimensions: Continuous Self-Similar Solutions
• Gravitational collapse of a spherical scalar field
• Critical phenomena in gravitational collapse with competing scalar field and gravitational waves, in 4+1 dimensions
• New results on the dynamics of critical collapse
• Critical spacetime crystals in continuous dimensions