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.
Physical Review D
- Pub Date:
- October 1997
- Einstein-Maxwell spacetimes spacetimes with fluids radiation or classical fields;
- Exact solutions;
- General Relativity and Quantum Cosmology
- 18 pages, ReVTeX. To appear in Physical Review D. Significant changes include more details in the derivations of certain key equations and the addition of an appendix containing a proof of the existence of a geon solution to the equations derived by Wheeler. Also a reference has been added and various minor changes have been made