Probing the gravitational geon

TL;DR

This paper critically analyzes the Brill-Hartle gravitational geon model, demonstrating that high-frequency gravitational waves cannot form a non-singular spherical geon, impacting theories of gravitational energy.

Contribution

It provides a formal analysis showing the impossibility of constructing a non-singular spherical gravitational geon using high-frequency waves.

Findings

High-frequency waves are necessary for geon formation.

Spherical shell in the geon model is singular and non-regular.

High symmetry is incompatible with stable geon solutions.

Abstract

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 gravitational wave perturbations of the spherical background as a superposition of tensor spherical harmonics and an attempt is made to build a non-singular solution to meet the requirements of a gravitational geon. 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 contrasted. The spherical shell in the proposed Brill-Hartle geon does not meet the regularity conditions required for a non-singular 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 non-viability, 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.