Critical-mass attainment and supercritical collapse range

Determine whether the Chandrasekhar mass itself belongs to the set of masses admitting a finite-energy radial order-22 classical physical-vacuum solution whose full support collapses to the origin in finite time, and whether every mass greater than the Chandrasekhar mass belongs to that set.

Background

The paper defines $\mathscr S_{22}$ as the set of masses for which the exact Chandrasekhar Euler–Poisson system admits a finite-energy radial order-22 classical physical-vacuum solution whose full support radius tends to zero at a finite time. The authors prove that $\inf \mathscr S_{22}=M_{\rm Ch}$: subcritical masses cannot undergo complete support collapse by an energy lower bound, while all masses in a sufficiently small interval immediately above $M_{\rm Ch}$ are realized by the constructed collapsing solutions.

The result does not establish whether the infimum is attained, i.e. whether a complete-collapse solution exists exactly at $M_{\rm Ch}$, nor whether the constructed near-critical interval can be extended to every supercritical mass. These two questions are explicitly left unresolved.