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arXiv 0910.0926gr-qchep-th
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弱引力场中的静电学问题

Aspects of electrostatics in a weak gravitational field

Hamsa Padmanabhan, T. Padmanabhan

摘要:

利用Rindler度规模拟引力场,讨论了均匀弱引力场中点带电粒子的静电特性。一些以前已知的结果是通过更简单和更透明的程序获得的,并以直观的方式进行解释。具体而言:(i)我们证明了在Rindler坐标系中静止电荷的静电势可表示为A_0=(q/l),其中l是从电荷到场点沿零测地线的仿射参数距离。(ii)我们得到了Rindler坐标系中一个电荷对另一个电荷所施加的静电力之和,并讨论了它的解释。(iii)我们展示了一个纯粹的静电项在林德勒框架出现作为一个辐射项在惯性框架。(In这部分是因为在弱引力场中静止的电荷由于它们的静电能而具有额外的重量。这个重量与加速度成正比,与距离成反比--这是辐射场的通常特征。)(iv)我们还解释了辐射反应项的起源,通过扩展我们的方法,包括一个缓慢变化的加速度。这些结果中的许多可能有可能的情况下,在任意静态几何静电的扩展。[摘要]

英文摘要:

Several features of electrostatics of point charged particles in a weak, homogeneous, gravitational field are discussed using the Rindler metric to model the gravitational field. Some previously known results are obtained by simpler and more transparent procedures and are interpreted in an intuitive manner. Specifically: (i) We show that the electrostatic potential of a charge at rest in the Rindler frame is expressible as A_0=(q/l) where l is the affine parameter distance along the null geodesic from the charge to the field point. (ii) We obtain the sum of the electrostatic forces exerted by one charge on another in the Rindler frame and discuss its interpretation. (iii) We show how a purely electrostatic term in the Rindler frame appears as a radiation term in the inertial frame. (In part, this arises because charges at rest in a weak gravitational field possess additional weight due to their electrostatic energy. This weight is proportional to the acceleration and falls inversely with distance -- which are the usual characteristics of a radiation field.) (iv) We also interpret the origin of the radiation reaction term by extending our approach to include a slowly varying acceleration. Many of these results might have possible extensions for the case of electrostatics in an arbitrary static geometry. [Abridged Abstract]

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