标题： 关于引力场的能量-动量张量 显示英文标题

标题： On energy-momentum tensors of gravitational field

摘要： 在最低近似下考虑并比较了引力场的几个能量-动量“张量”。当粒子的运动方程与广义相对论中的相同时，每个张量与点状粒子的能量-动量张量一起满足守恒定律。结果显示，在牛顿近似下，这些张量之间的差异在于它们的能量密度在相互作用能量密度（仅在粒子位置处非零）和引力场能量密度之间的分布方式。从洛伦兹不变性出发，考虑了自旋为2、质量为0的场的拉格朗日量。它们之间仅相差散度。通过Belinfante-Rosenfeld方法，从这些拉格朗日量中构造出能量-动量张量。使用每个张量在三重引力子顶点中，我们得到了在$G^2$近似下的牛顿中心度规。这些“场理论”张量中只有一个（即Thirring张量和由Misner、Thorne和Wheeler给出的拉格朗日量得到的张量的半和）给出了正确的近日点进动值。这个张量与Weinberg的张量不一致（可直接从爱因斯坦方程得到），并且给出了一个球形物体的度规，在第一非线性近似中其空间部分与和谐坐标下的Schwarzschild场不同。因此，这种场中的相对论粒子必须按照不同于广义相对论的规则运动。这种方法使引力能量-动量张量与其他任何能量-动量张量处于同等地位。 显示英文摘要

摘要： Several energy-momentum "tensors" of gravitational field are considered and compared in the lowest approximation. Each of them together with energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from the other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Starting from Lorentz invariance the Lagrangians for spin-2, mass-0 field are considered. They differ only by divergences. From these Lagrangians by Belinfante-Rosenfeld procedure the energy-momentum tensors are build. Using each of these tensors in 3-graviton vertex we obtain the corresponding metric of a Newtonian center in $G^2$ approximation. Only one of these ''field-theretical''tensors (namely the half sum of Thirring tensor and tensor obtained from Lagrangian given by Misner, Thorne and Wheeler) leads to correct value of the perihelion shift. This tensor does not coincide with Weinberg`s one (directly obtainable from Einstein equation) and gives metric of a spherical body differing (in space part of metric in the first nonlinear approximation) from Schwarzschild field in harmonic coordinates. As a result a relativistic particle in such field must move note according general relativity prescriptions. This approach puts the gravitational energy-momentum tensor on the same footing as any other energy-momentum tensor.