Does a dynamical system lose energy by emitting gravitational waves?

We note that Eddington's radiation damping calculation of a spinning rod fails to account for the complete mass integral as given by Tolman. The missing stress contributions precisely cancel the standard rate given by the 'quadrupole formula'. This indicates that while the usual 'kinetic' term can properly account for dynamical changes in the source, the actual mass is conserved. Hence gravity waves are not carriers of energy in vacuum. This supports the hypothesis that energy including the gravitational contribution is confined to regions of non-vanishing energy-momentum tensor $T_{ik}$. PACS numbers: 04.20.Cv, 04.30.-wComment: Published in Modern Physics Letters A vol 14, no 23, 1531, 1999 Full text available in the journa

Stability of Gravitational and Electromagnetic Geons

Recent work on gravitational geons is extended to examine the stability properties of gravitational and electromagnetic geon constructs. All types of geons must possess the property of regularity, self-consistency and quasi-stability on a time-scale much longer than the period of the comprising waves. Standard perturbation theory, modified to accommodate time-averaged fields, is used to test the requirement of quasi-stability. It is found that the modified perturbation theory results in an internal inconsistency. The time-scale of evolution is found to be of the same order in magnitude as the period of the comprising waves. This contradicts the requirement of slow evolution. Thus not all of the requirements for the existence of electromagnetic or gravitational geons are met though perturbation theory. From this result it cannot be concluded that an electromagnetic or a gravitational geon is a viable entity. The broader implications of the result are discussed with particular reference to the problem of gravitational energy.Comment: 40 pages, 5 EPS figures, uses overcite.st

The Energy of a Dynamical Wave-Emitting System in General Relativity

The problem of energy and its localization in general relativity is critically re-examined. The Tolman energy integral for the Eddington spinning rod is analyzed in detail and evaluated apart from a single term. It is shown that a higher order iteration is required to find its value. Details of techniques to solve mathematically challenging problems of motion with powerful computing resources are provided. The next phase of following a system from static to dynamic to final quasi-static state is described.Comment: 36 pages, 2 figures, to appear in Foundations of Physic

Extended Planck Scale

Traditional derivations of the Planck mass ignore the role of charge and spin in general relativity. From the Kerr-Newman null surface and horizon radii, quantized charge and spin dependence are introduced in an extended Planck scale of mass. Spectra emerge with selection rules dependent upon the choice of Kerr-Newman radius to link with the Compton wavelength. The appearance of the fine structure constant suggests the possibility of a variation in time of the extended Planck mass, which may be much larger than the variation in the traditional one. There is a suggestion of a connection with the $\alpha$ value governing high-energy radiation in Z-boson production and decay.Comment: 9 page

The New Planck Scale: Quantized Spin and Charge Coupled to Gravity

In the standard approach to defining a Planck scale where gravity is brought into the quantum domain, the Schwarzschild gravitational radius is set equal to the Compton wavelength. However, ignored thereby are the charge and spin, the fundamental quantized aspects of matter. The gravitational and null-surface radii of the Kerr-Newman metric are used to introduce spin and charge into a new extended Planck scale. The fine structure constant appears in the extended Planck mass and the recent discovery of the $\alpha$ variation with the evolution of the universe adds further significance. An extended Planck charge and Planck spin are derived. There is an intriguing suggestion of a connection with the $\alpha$ value governing high-energy radiation in Z-boson production and decay.Comment: 8 pages, This essay received an "honourable mention" in the 2003 Essay Competition of the Gravity Research Foundatio

General relativistic velocity: the alternative to dark matter

We consider the gravitational collapse of a spherically symmetric ball of dust in the general relativistic weak gravity regime. The velocity of the matter as viewed by external observers is compared to the velocity gauged by local observers. While the comparison in the case of very strong gravity is seen to follow the pattern familiar from studies of test particles falling towards a concentrated mass, the case of weak gravity is very different. The velocity of the dust that is witnessed by external observers is derived for the critically open case and is seen to differ markedly from the expectations based upon Newtonian gravity theory. Viewed as an idealized model for a cluster of galaxies, we find that with the general relativistic velocity expression, the higher-than-expected constituent velocities observed can be readily correlated with the solely baryonic measure of the mass, obviating the need to introduce extraneous dark matter. Hitherto unexplained and subject-to-reinterpretation astrophysical phenomena could also be considered within this context. It is suggested that an attempt be made to formulate an experimental design at smaller scales simulating or realizing a collapse with the aim of implementing a new test of general relativity.Comment: 12 pages, 2 figure