= Extremal Euclidean throat
{title2=$V(r)\sim a(r-r_h)^2,\quad\int dr/\sqrt V\to\infty$}
At a degenerate static horizon the Euclidean proper radial distance diverges logarithmically, so the horizon is an infinite end rather than a finite polar origin. Its time circle is not contracted at a conical tip, and local cone regularity imposes no finite period. The vanishing limiting <surface gravity> determines zero Hawking temperature; the simple-horizon periodicity argument must not be applied unchanged at the degenerate root.
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