标题： 引力的四维矢量理论中的能量和动量 显示英文标题

标题： Energy and Momentum in the Tetrad Theory of Gravitation

摘要： 我们研究了孤立系统在四维标架引力理论中的能量和动量，从最一般的关于扭率二次的拉格朗日量出发，该拉格朗日量包含四个未知参数。 当应用于静态球对称情况时，平行矢量场呈对角形式，场方程有一个精确解。 我们在不假设系统任何对称性质的情况下，分析了远离孤立系统的真空中的线性化场方程。 线性化方程是一组对称和反对称张量场的耦合方程，但对于稳态情况，可以将其解到$O(1/r)$。 发现一般解包含两个常数，一个是源的引力质量，另一个是一个常矢量${\grave B_\alpha}$。 从这个解中计算出总能量，发现它等于源的引力质量。 我们还计算了空间动量，发现其值与常矢量${\grave B_\alpha}$相同。 在远离源的距离处有效的真空线性化场方程，并没有给出关于常矢量${\grave B_\alpha}$是否为零的任何信息。 对于一个弱引力源，其场在所有地方都很弱，我们发现常矢量${\grave B_\alpha}$为零。 显示英文摘要

摘要： We study the energy and momentum of an isolated system in the tetrad theory of gravitation, starting from the most general Lagrangian quadratic in torsion, which involves four unknown parameters. When applied to the static spherically symmetric case, the parallel vector fields take a diagonal form, and the field equation has an exact solution. We analyze the linearized field equation in vacuum at distances far from the isolated system without assuming any symmetry property of the system. The linearized equation is a set of coupled equations for a symmetric and skew-symmetric tensor fields, but it is possible to solve it up to $O(1/r)$ for the stationary case. It is found that the general solution contains two constants, one being the gravitational mass of the source and the other a constant vector ${\grave B_\alpha}$. The total energy is calculated from this solution and is found to be equal to the gravitational mass of the source. We also calculate the spatial momentum and find that its value coincides with the constant vector ${\grave B_\alpha}$. The linearized field equation in vacuum, which is valid at distances far from the source, does not give any information about whether the constant vector ${\grave B_\alpha}$ is vanishing or not. For a weakly gravitating source for which the field is weak everywhere, we find that the constant vector ${\grave B_\alpha}$ vanishes.