Static potential across a compact circle
= Static potential across a compact circle
{title2=$U(r)=C\pi\coth(\pi r/L)/(Lr)$}
On three noncompact spatial dimensions times a circle of circumference $L$, the <method of images> gives $\sum_{j\in\mathbb Z}[r^2+j^2L^2]^{-1}=\pi\coth(\pi r/L)/(Lr)$ at equal compact coordinates. This interpolates from $1/r^2$ at short distances to $\pi/(Lr)$ at long distances. A gravitational circle-radius scalar can change the long-range coefficient if it remains unstabilized.