Method of the SelfConsistent Field in General Relativity and its Application to the Gravitational Geon
Abstract
Concentrations of radiation held together for a long time by their own gravitational attraction ("geons") have been studied for nearly a decade. We extend the previous analyses to the case where gravitational waves are the source of the geon's mass energy. To analyze these solutions of the freespace Einstein equations with persistent features, we develop an approximation method to treat small ripples on a strongly curved background metric. The background metric describes the largescale persistent features of the geon and is taken to be spherically symmetric. The waves superimposed on this background have an amplitude small enough so that their dynamics can be analyzed in the linear approximation; however, their wavelength is so short, and their time dependence so rapid that their energy is appreciable and produces the strongly curved background metric in which they move. The Einstein equations are investigated in this limit of short wavelength. It is found that the largescale features of thinshell spherical gravitational geonsin fact, of thinshell spherical geons constructed from any field of zero rest massare identical to those of the spherical electromagnetic geons analyzed previously.
 Publication:

Physical Review
 Pub Date:
 July 1964
 DOI:
 10.1103/PhysRev.135.B271
 Bibcode:
 1964PhRv..135..271B