Initial-Value Problem on Einstein-Rosen Manifolds

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Abstract
A class of solutions of the time-symmetric initial-value equations for gravitation and electromagnetism is obtained on a two-sheeted manifold containing N Einstein-Rosen bridges. The initial metric tensor and electric field are expressed in terms of a pair of harmonic functions, called ``metric potentials,'' which are required to be analytic and asymptotically flat and to satisfy certain match-up conditions; these potentials are then determined by applying the method of inversion images. The particular case of two identical Einstein-Rosen bridges is examined in detail, and is shown to correspond to a wormhole in an asymptotically flat (one-sheeted) universe. A charge and ``renormalized mass'' are defined for each Einstein-Rosen bridge, as well as an interaction energy (gravitational plus electrostatic potential energy) for the system as a whole. Expressions for these and other physical characteristics are evaluated explicitly in the two-body case.