Hyperbolic-space Coulomb field
= Hyperbolic-space Coulomb field
{title2=$E(\xi)=Q/[4\pi\epsilon_0R^2\sinh^2(\xi/R)]$}
In static time times round three-dimensional <hyperbolic space> of curvature radius $R$, a geodesic sphere has area $4\pi R^2\sinh^2(\xi/R)$. The <Gauss law> therefore gives the displayed radial field. It approaches the flat-space inverse-square field near the charge and falls exponentially at large geodesic distance. The curvature changes the area of a sphere, not the conserved flux.