Conical singularity
= Conical singularity
{title2=$ds^2=dR^2+a^2R^2d\vartheta^2$}
A conical singularity is a failure of smoothness at the apex of a metric cone. If $\vartheta$ has period $P$, small circles have circumference-to-radius ratio $aP$. The two-dimensional apex is smooth precisely when this equals $2\pi$. <Euclidean black-hole regularity condition> applies this test to the imaginary-time and radial plane.