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arXiv 0802.2697gr-qc
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遥平行引力中的引力磁学

Gravitomagnetism in teleparallel gravity

E. P. Spaniol, V. C. de Andrade

摘要:

物质电荷和电流可以产生场的假设可以追溯到广义相对论(GR)的起源。另一方面,作为一种规范理论,基于规范场的强度分量,广义相对论的遥平行等效(TEGR)似乎是定义这些场的理想方案。目前的工作的目的是调查的性质的引力电场和磁场的背景下的TEGR,其中的四元组形式主义背后似乎更适合于处理与观察者有关的现象。作为我们的主要结果,我们首次得到了史瓦西解的引力电磁场的精确表达式,它在线性近似下成为通常所期望的。为了加深我们对这些场的理解,我们还研究了慢运动和弱场区域中旋转球壳产生的几何。同样,所得到的表达式与电磁学的表达式完全一致。

英文摘要:

The assumption that matter charges and currents could generate fields, which are called, by analogy with electromagnetism, gravitoeletric and gravitomagnetic fields, dates from the origins of General Relativity (GR). On the other hand, the Teleparallel Equivalent of GR (TEGR), as a gauge theory, seems to be the ideal scenario to define these fields, based on the gauge field strength components. The purpose of the present work is to investigate the nature of the gravitational electric and magnetic fields in the context of the TEGR, where the tetrad formalism behind it seems to be more appropriated to deal with phenomena related to observers. As our main results, we have obtained, for the first time, the exact expressions for the gravito-electromagnetic fields for the Schwarzschild solution that in the linear approximation become the usual expected ones. To improve our understanding about these fields, we have also studied the geometry produced by a spherical rotating shell in slow motion and weak field regime. Again, the expressions obtained are in complete agreement with those of electromagnetism.

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