Narrow Results

In physics, the application of the regular cases of spacelike fronts has been studied extensively; however, under the gravitational influence, the spacelike fronts can be singular. In this paper, we will consider the traveling trajectories of a set of parallel light rays as spacelike fronts with singularities in null de Sitter sphere. It is of great significance to investigate and explore the spacelike fronts which may have singularities in null de Sitter sphere. We also characterize the singularities of the nullcone dual worldsheets generated by spacelike fronts via the spherical curvature. Then we define the nullcone caustics and analyze the geometric properties of the nullcone caustics at singular points. Moreover, we establish the dual relationship between spacelike fronts and the nullcone dual worldsheets.