The purpose of this paper is to illustrate the problem of energy and momentum distributions of Van Stockum space-time within the framework of two different theories of gravity, general relativity and teleparallel gravity. We have shown that for all homogeneous space-times with metric components \(g_{\mu \nu }\) being functions of time variable, t, alone and independent of space variables the total gravitational energy for any finite volume is identically zero. By working with general relativity, we have calculated the energy-momentum density for Van Stockum space-time using double index complexes and in the framework teleparallel gravity, we used the energy-momentum complexes of Einstein, Bergmann–Thomson and Landau–Lifshitz. In our analysis, we sustained that general relativity and teleparallel gravity are equivalent theories of space-time under consideration. For space-time under consideration, we have shown that different complexes of energy-momentum density do not provide the same results neither in general relativity nor in teleparallel gravity.

本文的目的是在两种不同的引力理论（广义相对论和远平行引力）的框架下，说明范斯托克姆时空的能量和动量分布问题。我们已经表明，对于所有齐次时空，度量分量\（g _ {\ mu \ nu} \）是时间变量t的函数单独且不依赖于空间变量的情况下，任何有限体积的总重力能量都为零。通过广义相对论，我们使用双指数复合物计算了Van Stockum时空的能量动量密度，在远平行重力框架下，我们使用了爱因斯坦，伯格曼-汤姆森和兰道-利夫希茨的能量动量复合物。在我们的分析中，我们坚持认为广义相对论和远平行重力是所考虑的时空等效理论。对于所考虑的时空，我们已经表明，不同的能量动量密度复合物在广义相对论和远平行重力中都不能提供相同的结果。