= Static closed cosmic-string universe
{title2=$\rho_s a^2=3K/(8\pi G)$}
A closed universe containing only a <cosmic string network> can remain static. Its <Friedmann acceleration equation> vanishes identically because $P_s=-\rho_s/3$, and its <Friedmann equation> requires $\rho_s a^2=3K/(8\pi G)$. Once this conserved normalization is tuned, every positive radius gives a static solution. The usual Hubble-normalized <cosmological density parameter> is undefined at a static epoch.
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