= Low-density polytropic mass divergence
{title2=$M\propto\rho_c^{(3-n)/(2n)}$}
For $p=K\rho^{1+1/n}$, the <Lane-Emden mass formula> gives $M\propto\rho_c^{(3-n)/(2n)}$ at fixed $K$, while $M/R\propto\rho_c^{1/n}$. For $3<n<5$, the <Lane-Emden equation> has a finite-radius solution, yet $M\to\infty$ as $\rho_c\to0$. The relativistic <Tolman–Oppenheimer–Volkoff equation> approaches this limit since $p_c/\rho_c\to0$. Monotone pressure and density alone therefore do not impose a finite stellar maximum mass.
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