Bifurcation surface of the observation point, P, its cusp locus, and the light cylinder r = c/ω. (a) In contrast to the envelope of wave fronts shown in Fig. 4a, which resides in the space of observation points, the surface shown here resides in the space of source points: it is the locus of source elements that approach P along the radiation direction at the speed of light at the retarded time. The two sheets of this surface meet along a cusp that tangentially touches the light cylinder where it crosses the plane of rotation containing the observation point and spirals outwards as the colatitude, θ, decreases. The source points on this cusp approach the observer along the radiation direction not only at the speed of light but also with zero acceleration at the retarded time. (b) Close-up view of the two sheets of the bifurcation surface in the vicinity of the cusp locus of this surface. The hyperboloid containing this cusp has the conical asymptotes θ = arcsin[c/(r_Pω)] and θ = π − arcsin[c/(r_Pω)].