Quantum critical collapse in the large D limit
Abstract
In analytically tractable models of Einstein-scalar critical collapse, it has been shown that the quantum self-energy of the collapsing matter in the dominant s-wave sector grows with Lyapunov exponent D−2, eventually competing with the classical instability that controls black hole formation. This competition shifts the naked singularity threshold and produces a finite mass gap within semiclassical control, yet that control may appear threatened as the spacetime dimension D→∞. We study this quantum growing mode in both continuously (CSS) and discretely (DSS) self-similar critical spacetimes at large D and establish that the universal Lyapunov exponent survives both forms of self-similarity. In CSS, the classical approach to a naked singularity is interrupted by the appearance of trapped surfaces. At large D, the horizon tracing reduces to a Bessel problem, yielding a quantum wall whose radius obeys rh∝(D−2)−2. This radius can remain above the Planck scale at finite D, although maintaining this hierarchy becomes increasingly demanding as D grows. In DSS, the same growth is modulated by echoing and can retain memory of previous echoes. The simplest anomaly-induced action exhibits accumulating memory but is singular at the spherical center. We construct a covariant one-loop action whose stress tensor remains smooth throughout the DSS domain and organize it into an echo-periodic structure without memory. This suggests that the smooth vacuum polarization of the genuine four-dimensional DSS Choptuik spacetime may similarly be governed by its exact echoing symmetry.
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BibTeX
@misc{wu2026quantum,
title = {{Quantum critical collapse in the large $D$ limit}},
author = {Chih-Hung Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20705},
eprint = {2610.20705},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20705},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum critical collapse in the large D limit
AU - Chih-Hung Wu
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20705
UR - https://arxiv.org/abs/2610.20705
AB - In analytically tractable models of Einstein-scalar critical collapse, it has been shown that the quantum self-energy of the collapsing matter in the dominant s-wave sector grows with Lyapunov exponent D−2, eventually competing with the classical instability that controls black hole formation. This competition shifts the naked singularity threshold and produces a finite mass gap within semiclassical control, yet that control may appear threatened as the spacetime dimension D→∞. We study this quantum growing mode in both continuously (CSS) and discretely (DSS) self-similar critical spacetimes at large D and establish that the universal Lyapunov exponent survives both forms of self-similarity. In CSS, the classical approach to a naked singularity is interrupted by the appearance of trapped surfaces. At large D, the horizon tracing reduces to a Bessel problem, yielding a quantum wall whose radius obeys r_h∝(D−2)^−2. This radius can remain above the Planck scale at finite D, although maintaining this hierarchy becomes increasingly demanding as D grows. In DSS, the same growth is modulated by echoing and can retain memory of previous echoes. The simplest anomaly-induced action exhibits accumulating memory but is singular at the spherical center. We construct a covariant one-loop action whose stress tensor remains smooth throughout the DSS domain and organize it into an echo-periodic structure without memory. This suggests that the smooth vacuum polarization of the genuine four-dimensional DSS Choptuik spacetime may similarly be governed by its exact echoing symmetry.
ER -