Bootstrap Gravitational Geons

Abstract

It is shown that there exist solutions of the vacuum Einstein field equations with the property that exterior to the Schwarzschild radius, $R=2m$, the solution appears to be that of a static spherically symmetric particle of mass $m$ (that is, strictly Schwarzschild), whereas interior to the Schwarzschild radius the topology remains Euclidean and the solutions have the property of a bundle of gravitational radiation so intense that the mutual gravitational attraction of the various parts of the bundle prevent the radiation from spreading beyond the Schwarzschild radius. It is not known whether there exist solutions of this type which remain nonsingular for all times; however, no singularity can ever be observed exterior to the Schwarzschild radius. The Cauchy data for one such solution are explicity exhibited.