Relativistic Virial Theorem, Limiting Compactness, and the end state of gravitational collapse

It is noteworthy that limiting compactness of a static bounded configuration is characterized by a general principle: $\mathit{\text{one,}}\mathit{\text{by}}\mathit{\text{equipartition}}\mathit{\text{of}}\mathit{\text{mass}}\mathit{\text{between}}\mathit{\text{inside}}\mathit{\text{and}}\mathit{\text{outside,}}\mathit{\text{and}}\mathit{\text{the}}\mathit{\text{other}}\mathit{\text{by}}\mathit{\text{vanishing}}\mathit{\text{of}}\mathit{\text{energy}}\mathit{\text{inside.}}$ The former implies gravitational energy being half of mass leading to limiting compactness $M\mathrm{/}R=4\mathrm{/}9$ of Buchdahl star while for the latter, the two are equal giving $M\mathrm{/}R=1\mathrm{/}2$ of black hole with horizon. \emph{This is the relativistic Virial theorem respectively for massive and massless particles.} It is remarkable that it prescribes that there can exist only two equilibrium states which also define limiting compactness of the object. Consequently, it leads to a profound prediction that the ultimate endproduct of gravitational collapse could only be one of the two, Buchdahl star or black hole.