 Tangential critical curve of an axisymmetric lens

For circular reduced deflection $\alpha (r)=r\bar{\kappa }(r)$, a displacement perpendicular to the radial direction is multiplied by $1-\bar{\kappa }$. Vanishing of this eigenvalue gives a tangential gravitational-lensing critical curve. Its source position is $\beta =r-\alpha (r)=0$, so its caustic is the origin in the circular model. Near it, images are stretched tangentially into arcs or an Einstein ring.