Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8810Research ArticleStudy Solutions of the Geodesic Equations for a Model of a Point Source of Gravity in the Empty SpacePopovN N-BashlykovA M-MorozI I-Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RASState University “Moscow Institute of Physics and Technology”1504201349510008092016Copyright © 2013,2013In this paper the properties of solutions of the geodesic equations for a model of a point source of gravity, radiating heat are studied. Geodesic equations are constructed using a metric which is the solution of equations that represent the zero trace of the Ricci tensor. These equations are a generalization of Einstein’s equations in vacuum. They allow to obtain solutions in the form of non-stationary spherically symmetric metrics, whose components are a function of two variables. The ordinary system of diﬀerential equations of second order for surveying natural parameter consists of four equations. It can be partially integrated and reduced to a system of two second order diﬀerential equations. By substitution method the system is reduced to a pair of diﬀerential equations in partial derivatives of the two unknown variables. Finally, we obtain one quasi-linear equation. In the normal case, equations of this type form gaps with limited solutions. However, the numerical calculations show that the solutions can also become unrestricted due to the pecularities in the right parts.spherically symmetric spacenon-stationary metricgeodesicHopf equationnon-linear characteristic curvesсферически симметричное пространствонестационарная метрикагеодезическиеуравнение Хопфанелинейные характеристические кривые