Oscillatory Character of Reissner-Nordström Metric for an Ideal Charged Wormhole

Abstract

A transformation is presented to remove coordinate ("pseudo") singularities from metrics of a certain class, a special case of which is the transformation of Kruskal, extending the Schwarzschild metric beyond its pseudosingularity. The transformation is applied to the Reissner-Nordstr\"om metric, which describes a concentration of charge and mass in general relativity. On an initial surface this metric shows the same general behavior as the Schwarzschild metric, describing a "wormhole," or bridge, between two asymptotically flat spaces, but with electric flux flowing through the wormhole. It is found that the region of minimum radius, the so-called "throat" of the wormhole, begins to contract, but reaches a minimum and re-expands after a finite proper time, rather than pinching off as in the Schwarzschild-Kruskal case: the raduis of the throat pulsates periodically in time, "cushioned" by Maxwell pressure of the electric field through the throat. The motion of charged particles in this metric is investigated, and it is shown that no particle can hit the geometric singularity at $r=0$; (1) quite in general, provided only that the mass of the test particle exceeds the value associated in general relativity with its charge, and (2) in particular when the test particle has no charge at all, but (3) such collisions are not avoided when the throat itself is not endowed with any electric flux.