Isolated systems in general relativity : the gravitational-electrostatic two-body balance problem and the gravitational geon




Perry, George Philip

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This dissertation examines two fundamentally different types of isolated systems in general relativity. In part 1, an exact solution of the Einstein-Maxwell equations representing the exterior field of two arbitrary charged essentially spherically symmetric (Reissner-Nordström) bodies in equilibrium is studied. Approximate solutions representing the gravitational- electrostatic balance of two arbitrary point sources in general relativity have led to contradictory arguments in the literature with respect to the condition of balance. Up to the present time, the only known exact solutions which can be interpreted as the nonlinear superposition of two Reissner-Nordström bodies without an intervening strut has been for critically charged masses, [special characters omitted]. In this dissertation . the invariant physical charge for each source is found by direct integration of Maxwell's equations. The physical mass for each source is invariantly defined in a manner similar to which the charge was found. It is shown that balance without tension or strut can occur for non-critically charged bodies. It is demonstrated that other authors have not identified the correct physical parameters for the masses and charges of the sources. Examination of the fundamental parameters of the space-time suggests a refinement of the nomenclature used to describe the physical properties is necessary. Such a refinement is introduced. Further properties of the solution, including the multipole structure and comparison with other parameterizations, are examined. Part 2 investigates the viability of constructing gravitational and electromagnetic geons: zero-rest-mass field concentrations, consisting of gravitational or electromagnetic waves, held together for long periods of time by their gravitational attraction. In contrast to an exact solution, the method studied involves solving the Einstein or Einstein-Maxwell equations for perturbations on a static background metric in a self-consistent manner. The Brill-Hartle gravitational geon construct as a spherical shell of small amplitude, high-frequency gravitational waves is reviewed and critically analyzed. The spherical shell in the proposed Brill-Hartle geon cannot be regarded as an adequate geon construct because it does not meet the regularity conditions required for a non-singular source. An attempt is made to build a non- singular solution to meet the requirements of a gravitational geon. Construction of a geon requires gravitational waves of high-frequency and the field equations are decomposed accordingly. A geon must also possess the property of quasi-stability on a time-scale longer than the period of the comprising waves. It is found that only unstable equilibrium solutions to the gravitational and electromagnetic geon problem exist. A perturbation analysis to test the requirement of quasi-stability resulted in a contradiction. Thus it could not be concluded that either electromagnetic or gravitational geons meet all the requirements for existence. The broader implications of the result are discussed with particular reference to the problem of with particular reference to the problem of gravitational energy.



General relativity (Physics), Gravitation