Numerical construction of a one-parameter family of discretely self-similar critical spacetimes for massless scalar collapse in continuous D>3, giving echoing period Delta(D) and Choptuik exponent gamma(D) with a maximum in Delta near D=3.76.
Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse
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abstract
We study the critical behaviour of spherically symmetric scalar field collapse to black holes in spacetime dimensions other than four. We obtain reliable values for the scaling exponent in the supercritical region for dimensions in the range $3.5\leq D\leq 14$. The critical exponent increases monotonically to an asymptotic value at large $D$ of $\gamma\sim0.466$. The data is well fit by a simple exponential of the form: $\gamma \sim 0.466(1-e^{-0.408 D})$.
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gr-qc 1years
2026 1verdicts
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Critical spacetime crystals in continuous dimensions
Numerical construction of a one-parameter family of discretely self-similar critical spacetimes for massless scalar collapse in continuous D>3, giving echoing period Delta(D) and Choptuik exponent gamma(D) with a maximum in Delta near D=3.76.