Caustic points of the timelike curve on the de Sitter 3-space

Abstract

In cosmology, de Sitter geometry is a model of an accelerated expansion of the universe. This geometry is obtained from the solution of the Einstein field equations with positive cosmological constant. This study focuses on the apparent shapes formed by reflecting the light rays emitted from the point light source according to the timelike mirror curve on the de Sitter 3-space. Then, the reflected light rays intersect at some points which are called singular points. We also have determined the patterns that corresponded to these singular points in the light source plane, namely the caustic points. We have examined the properties of the shapes formed by the caustic and singular points. Finally, a timelike mirror curve is presented on the de Sitter 3-space, and we visualize the projections of the shapes of its mirror images and caustics due to a point light source.