Interaction Energy in Geometrostatics
Abstract
The "geometrodynamical" description of particles by means of topological features of empty spacetime is applied here to the case of N charged masses which are momentarily at rest. These particles are represented by EinsteinRosen bridges in a mainfold which satisfies the timesymmetric initial value equations of gravitation and electromagnetism. Invariant definitions are given for the total mass energy of the system, and for the "bare mass" of each EinsteinRosen bridge. These masses characterize various asymptotically Schwarzschildian regions of the manifold and are, therefore, conserved in time. The total mass of the system differs from the sum of the bare masses by contributions from the gravitational and electrostatic interaction energies. It is shown that the interaction energy is always negative, and that it reduces to the classical expression in the limit of large separation between the masses. The shape of the minimal surface associated with each EinsteinRosen bridge, another invariant feature of the "particle," is discussed. The minimal surfaces are also used to characterize manifolds which can be interpreted as a closed universe containing N+1 "particles."
 Publication:

Physical Review
 Pub Date:
 July 1963
 DOI:
 10.1103/PhysRev.131.471
 Bibcode:
 1963PhRv..131..471B