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

Download: PDF

Submission history

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

Unique-IP document downloads: 4 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus