发表机构
Georgia Institute of Technology; Fudan University（佐治亚理工学院; 复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究对冷白矮星给出了钱德拉塞卡质量的动力学刻画，证明高于该质量时存在有限时间完全坍缩解，并构造了支撑收缩至原点、密度集中且内部趋近Goldreich-Weber轮廓的解，通过匹配渐近展开与能量估计完成证明。
AI 中文摘要
我们给出了由径向欧拉-泊松方程与精确钱德拉塞卡状态方程控制的冷白矮星的钱德拉塞卡质量的动力学刻画。该质量是使得具有物理真空的有限能量经典解能够在有限时间内将其整个支撑收缩到一点的质量的下确界。低于该质量时，能量守恒阻止完全坍缩。对于该质量之上足够小区间内的每一个质量，我们构造了一个解，其支撑收缩到原点，且密度在原点集中，携带恒星的全部质量。内部趋近于坍缩的Goldreich-Weber轮廓。在真空边界附近，不同的重标度给出了一个极限轮廓，该轮廓连接了压力定律的高密度和低密度区域。我们确定了该轮廓，并证明在加上电子静止能量后，守恒能量等于Goldreich-Weber参考解的能量。证明结合了匹配渐近展开与局部存在性和能量估计，这些估计将解从接近坍缩的时间向后延拓到一个共同的更早时间。
英文摘要
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.
Comments227 pages, minor revision
