Gravitational Geons Revisited

TL;DR

This paper reexamines gravitational geons, confirming their consistency, gauge invariance, and self-sufficiency within Einstein's equations, and extends understanding of their properties and solutions.

Contribution

It provides a detailed analysis confirming the gauge invariance and consistency of gravitational geons and offers an existence proof for these solutions.

Findings

Gravitational wave expansion is gauge invariant and consistent.

Geon solutions are self-consistent solutions to Einstein's equations.

Equations for gravitational geons match those derived by Wheeler for electromagnetic geons.

Abstract

A careful analysis of the gravitational geon solution found by Brill and Hartle is made. The gravitational wave expansion they used is shown to be consistent and to result in a gauge invariant wave equation. It also results in a gauge invariant effective stress-energy tensor for the gravitational waves provided that a generalized definition of a gauge transformation is used. To leading order this gauge transformation is the same as the usual one for gravitational waves. It is shown that the geon solution is a self-consistent solution to Einstein's equations and that, to leading order, the equations describing the geometry of the gravitational geon are identical to those derived by Wheeler for the electromagnetic geon. An appendix provides an existence proof for geon solutions to these equations.