arXiv 2108.021242021-08gr-qc

Fierz形式下线性化引力的能量动量张量和对偶对称性

Energy-momentum tensor and duality symmetry of linearized gravity in the Fierz formalism

Gabor Zsolt Toth

备注：: 45 pages, revised manuscript, title change
发表信息：: Classical and Quantum Gravity 39 (2022) 075003
DOI：: 10.1088/1361-6382/ac50eb

摘要：

本文详细讨论了平坦背景下的线性化引力公式，该公式以Fierz张量作为电磁场强度的对应，并用于研究线性化引力场的基本性质。特别地，线性化的爱因斯坦方程被写为根据Fierz张量的一阶偏微分方程，类似于一阶麦克斯韦方程组。对于线性化的引力场，发现了一个具有良好性质的能量动量张量（$T_{\mathrm{lg}}^{ab}$），它与电磁场的标准能量动量张量具有显著的相似性. $T_{\mathrm{lg}}^{ab}$在Fierz张量（由线性化度规的一阶导数构成）中是二次的，无迹的，并且在包含横向无迹规范的规范中满足主能量条件。它进一步表明，在适当的规范，包括横向无痕规范，线性化的重力在没有物质的对偶对称映射的菲尔斯张量，这是反对称的前两个指标，到其对偶。与线性化重力的规范和对偶对称性相关的守恒电流也被确定。这些电流与电动力学中的相应电流具有很好的相似性。

英文摘要：

A formulation of linearized gravity in flat background, based on the Fierz tensor as a counterpart of the electromagnetic field strength, is discussed in detail and used to study fundamental properties of the linearized gravitational field. In particular, the linearized Einstein equations are written as first order partial differential equations in terms of the Fierz tensor, in analogy with the first order Maxwell equations. An energy-momentum tensor ($T_{\mathrm{lg}}^{ab}$) with favourable properties and exhibiting remarkable similarity to the standard energy-momentum tensor of the electromagnetic field is found for the linearized gravitational field. $T_{\mathrm{lg}}^{ab}$ is quadratic in the Fierz tensor (which is constructed from the first derivatives of the linearized metric), traceless, and satisfies the dominant energy condition in a gauge that contains the transverse traceless gauge. It is further shown that in suitable gauges, including the transverse traceless gauge, linearized gravity in the absence of matter has a duality symmetry that maps the Fierz tensor, which is antisymmetric in its first two indices, into its dual. Conserved currents associated with the gauge and duality symmetries of linearized gravity are also determined. These currents show good analogy with the corresponding currents in electrodynamics.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文