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arXiv 0909.3336gr-qc
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5维Kaluza-Klein测地偏差方程的降维

Dimensional Reduction of the 5D Kaluza-Klein Geodesic Deviation Equation

V. Lacquaniti, G. Montani, F. Vietri

摘要:

在Kerner等人(2001)的工作中,面临着在5D Kaluza Klein背景中的测地线偏差问题。在Lorenz力的作用下,只要偏差矢量的第五分量满足一个额外的约束条件,并考虑到路径上的$q/m$守恒,所得方程的四维时空投影与通常的测地偏差方程一致,分析是在Kaluza-Klein模型中出现的标量场为常数的情况下进行的.在这里,我们专注于这样的工作的扩展到模型的存在下的标量场被认为是。当考虑最小情形$ϕ=1$时,我们的结果与Kerner等人的结果一致,而在一般情形下,我们的结果则有一些偏离.由于$ϕ$的存在的新颖性是,在两个测地线之间的$q/m$的变化是不保守的运动过程中,这样的行为的一个精确的法律已经推导出来。

英文摘要:

In the work of Kerner et al. (2001) the problem of the geodesic deviation in a 5D Kaluza Klein background is faced. The 4D space-time projection of the resulting equation coincides with the usual geodesic deviation equation in the presence of the Lorenz force, provided that the fifth component of the deviation vector satisfies an extra constraint which takes into account the $q/m$ conservation along the path. The analysis was performed setting as a constant the scalar field which appears in Kaluza-Klein model. Here we focus on the extension of such a work to the model where the presence of the scalar field is considered. Our result coincides with that of Kerner et al. when the minimal case $ϕ=1$ is considered, while it shows some departures in the general case. The novelty due to the presence of $ϕ$ is that the variation of the $q/m$ between the two geodesic lines is not conserved during the motion; an exact law for such a behaviour has been derived.

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