Singularity in the relativistic celestial dynamics

Abstract

This article studies the singularity in the relativistic celestial dynamics. For the relativistic N-body system, we prove the nonexistence of noncollision-singularities. We demonstrate approaching the light speed within finite time is equivalent to the occurrence of a collision. We also introduce the spiral vector to describe the behavior of 2-collisions. We prove the improbability of the 2-collision singularities with zero spiral vectors. By constructing singularities, we prove the Lebesgue measure of singularities is infinity and singularities are of the second Baire category. The singularities are not negligible in the measure-theoretic or the topological sense, and we thus solve Littlewood's thirteenth problem in the relativistic situation.