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.