Probing the gravitational geon

The Brill-Hartle gravitational geon construct as a spherical shell of small amplitude, high frequency gravitational waves is reviewed and critically analyzed. The Regge-Wheeler formalism is used to represent the most general gravitational wave perturbations of the spherical background as a superposition of tensor spherical harmonics and an attempt is made to build a nonsingular solution to meet the requirements of a gravitational geon. The attempted constructs of gravitational and electromagnetic geons are contrasted. High-frequency waves are seen to be a necessary condition for the geon and the field equations are decomposed accordingly. It is shown that this leads to the impossibility of forming a spherical gravitational geon. The attempted constructs of gravitational and electromagnetic geons are constructed. The spherical shell in the proposed Brill-Hartle geon does not meet the regularity conditions required for a nonsingular source and hence cannot be regarded as an adequate geon construct. Since it is the high frequency attribute which is the essential cause of the geon nonviability, it is argued that a geon with less symmetry is an unlikely prospect. The broader implications of the result are discussed with particular reference to the problem of gravitational energy.