论文标题
关于Finsler空间中应力能量张量的重要性
On the significance of the stress-energy tensor in Finsler spacetimes
论文作者
论文摘要
我们重新审视了从洛伦兹 - 芬斯勒设置$（m，l）$开始的物理论点，从而导致了从经典相对论开始的洛伦兹 - 芬特勒设置$（m，l）$的定义。使用流体的标准启发式方法和拉格朗日式方法都已考虑在内。特别是，我们认为，lorentz对称性的Finslerian破裂使$ t $ t $成为各向异性2 tensor（即，每个$ l $ -timelike方向的张量），与$ m $定义的能量摩托车矢量相反。将这种张量与使用拉格朗日方法获得的不同张量进行了比较。从几何观点修改了分歧的概念，然后重新审视每个观察者领域的$ t $的保护法。我们引入了自然的{\ em各向异性Lie支架衍生}，该式}导致从音量元素获得的分歧和与$ L $相关的非线性连接获得的分歧。这种差异的计算选择了Chern各向异性连接，从而对文献中的先前选择给出了几何解释。
We revisit the physical arguments which lead to the definition of the stress-energy tensor $T$ in the Lorentz-Finsler setting $(M,L)$ starting at classical Relativity. Both the standard heuristic approach using fluids and the Lagrangian one are taken into account. In particular, we argue that the Finslerian breaking of Lorentz symmetry makes $T$ an anisotropic 2-tensor (i. e., a tensor for each $L$-timelike direction), in contrast with the energy-momentum vectors defined on $M$. Such a tensor is compared with different ones obtained by using a Lagrangian approach. The notion of divergence is revised from a geometric viewpoint and, then, the conservation laws of $T$ for each observer field are revisited. We introduce a natural {\em anisotropic Lie bracket derivation}, which leads to a divergence obtained from the volume element and the non-linear connection associated with $L$ alone. The computation of this divergence selects the Chern anisotropic connection, thus giving a geometric interpretation to previous choices in the literature.
