The interpretation of the C metric. The charged case whene2 ≤m2
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The charged C metric involves three parametersm, e andA representing mass, charge and acceleration respectively. Using a method developed in a previous paper, we show that whene2 ≤m2 the metric may be interpreted in terms of two Reissner-Nordström particles, each of massm and with charges +e and −e, in accelerated motion and connected by a spring. The method depends on the fact that for certain regions of the coordinate space the charged C metric may be transformed into the Weyl form for a static axisymmetric system. In this form the horizons of the C metric become line sources. One of the regions leads to a Weyl metric with two line sources, one of finite length which corresponds to the outer horizon of a Reissner-Nordström particle and the other semi-infinite corresponding to a horizon associated with uniform accelerated motion. A further coordinate transformation leads to a metric valid for a larger region of space-time in which there are two charged particles in accelerated motion. WhenAm is small, the electromagnetic invariants approximate to those for the Born field for two accelerated charges in special relativity.
KeywordsCharged Particle Differential Geometry Large Region Coordinate Transformation Special Relativity
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