Classical Physics


Weak Metric Fields

Authors: Valery Timin

In addition to the force fields defined by scalar and vector potential fields and their intensities, it is possible to have force fields defined directly through the metric tensor gij(r,t). The role of the metric tensor in the motion of a material point is that the trajectory between any two points of space–time along the geodesic "line" as the line of the smallest length is determined through it. The length of the "straight" corresponds to the length of the shortest "interval" between these points. The differential equation of this "shortest" condition is expressed by the Christoffel symbols. In this paper we consider the case of weak "metric" fields and velocities of the material point. The Christoffel symbols themselves and the metric field are defined as corresponding fields in Galilean space. Кроме силовых полей, задаваемых скалярным и векторным потенциальным полями и их напряженностями, возможно существование силовых полей, определяющихся непосредственно через метрический тензор gij(r,t). Роль метрического тензора в движении материальной точки заключается в том, что через него определяется траектория между любыми двумя точками пространства–времени по геодезической "прямой" как линии наименьшей длины. Длина "прямой" при этом соответствует длине наикратчайшего "интервала" между этими точками. Дифференциальное уравнение этого "наикратчайшего" условия выражается через символы Кристоффеля - В данной работе рассмотрен случай слабых "метрических" полей и скоростей движения материальной точки. Сами символы Кристоффеля и метрическое поле определены как соответствующие поля в галилеевом пространстве

Comments: language: Russian, number of pages: 7,, Creative Commons Attribution 3.0 License

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Submission history

[v1] 2019-08-04 15:12:03

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