Boundary-Geometry-Driven Black Hole Formation in Vacuum
Abstract
We identify a boundary-geometry-driven mechanism for the dynamical formation of marginally outer trapped surfaces (MOTSs) in vacuum general relativity. Mild three-dimensional anisotropies evolve inside a compact Cauchy domain whose effective isotropic thickness remains controlled, while the generalized boundary mean curvature can increase during either contracting or expanding boundary evolution. This drives the boundary across Yau's geometric threshold, forcing MOTS formation from initially untrapped data. We further interpret the characteristic shear construction of Ref.~\cite{MondalYau2026} as the null manifestation of the same anisotropic vacuum dynamics. The result provides a purely vacuum physical realization of MOTS formation through global geometric effects, without invoking a short-pulse concentration mechanism for gravitational radiation.
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BibTeX
@misc{dey2026boundarygeometrydriven,
title = {{Boundary-Geometry-Driven Black Hole Formation in Vacuum}},
author = {Dipanjan Dey and Puskar Mondal and Shing-Tung Yau},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02311},
eprint = {2609.02311},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02311},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Boundary-Geometry-Driven Black Hole Formation in Vacuum
AU - Dipanjan Dey
AU - Puskar Mondal
AU - Shing-Tung Yau
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02311
UR - https://arxiv.org/abs/2609.02311
AB - We identify a boundary-geometry-driven mechanism for the dynamical formation of marginally outer trapped surfaces (MOTSs) in vacuum general relativity. Mild three-dimensional anisotropies evolve inside a compact Cauchy domain whose effective isotropic thickness remains controlled, while the generalized boundary mean curvature can increase during either contracting or expanding boundary evolution. This drives the boundary across Yau's geometric threshold, forcing MOTS formation from initially untrapped data. We further interpret the characteristic shear construction of Ref.~\cite{MondalYau2026} as the null manifestation of the same anisotropic vacuum dynamics. The result provides a purely vacuum physical realization of MOTS formation through global geometric effects, without invoking a short-pulse concentration mechanism for gravitational radiation.
ER -