Modeling of the decay of binary trans-Neptunian objects belonging to the dynamically cold population of the classical Kuiper belt has been performed. We considered binary trans-Neptunian objects with masses 10 -10 , 10 -11 , 10 -12 , 10 -13 , 10 -14 of solar masses at component mass ratios of 1:1, 1:2, 1:10, 1:25 without taking into account tidal effects. Based on the results of numerical experiments, a criterion for the formation of a pair of trans-Neptunian objects in close orbits as a result of the decay of a binary ultra-wide trans-Neptunian object. Estimates of the relative distances, velocities of the components and the Kholshevnikov metric corresponding to the moment of the pair formation are obtained. This paper is based on a talk presented at VIII Bredikhin conference.