Collapse of white dwarfs above the Chandrasekhar mass
Abstract
We give a dynamical characterization of the Chandrasekhar mass for cold white dwarfs governed by the radial Euler--Poisson equations with the exact Chandrasekhar equation of state. This mass is the infimum of masses for which a finite-energy classical solution with a physical vacuum can contract its entire support to a point in finite time. Below it, conservation of energy prevents complete collapse. For every mass in a sufficiently small interval above it, we construct a solution whose support shrinks to the origin and whose density concentrates there with the full mass of the star. The interior approaches a collapsing Goldreich--Weber profile. Near the vacuum boundary, a different rescaling gives a limiting profile that connects the high- and low-density regimes of the pressure law. We determine this profile and show that, after adding the electron rest energy, the conserved energy equals that of the Goldreich--Weber reference solution. The proof combines matched asymptotic expansions with local existence and energy estimates that extend solutions backward from times approaching collapse to a common earlier time.
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BibTeX
@misc{chen2026collapse,
title = {{Collapse of white dwarfs above the Chandrasekhar mass}},
author = {Gong Chen and Zhiwu Lin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.34075},
eprint = {2609.34075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34075},
}
RIS
TY - UNPB
TI - Collapse of white dwarfs above the Chandrasekhar mass
AU - Gong Chen
AU - Zhiwu Lin
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2609.34075
UR - https://arxiv.org/abs/2609.34075
AB - We give a dynamical characterization of the Chandrasekhar mass for cold white dwarfs governed by the radial Euler--Poisson equations with the exact Chandrasekhar equation of state. This mass is the infimum of masses for which a finite-energy classical solution with a physical vacuum can contract its entire support to a point in finite time. Below it, conservation of energy prevents complete collapse. For every mass in a sufficiently small interval above it, we construct a solution whose support shrinks to the origin and whose density concentrates there with the full mass of the star. The interior approaches a collapsing Goldreich--Weber profile. Near the vacuum boundary, a different rescaling gives a limiting profile that connects the high- and low-density regimes of the pressure law. We determine this profile and show that, after adding the electron rest energy, the conserved energy equals that of the Goldreich--Weber reference solution. The proof combines matched asymptotic expansions with local existence and energy estimates that extend solutions backward from times approaching collapse to a common earlier time.
ER -