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Physics Essays, vol. 13, no. 4, 2000
It is shown that the 1915 Einstein equation is incompatible with the physical notion that a wave carries away energy-momentum. This proof is compatible with that Maxwell-Newton Approximation (the linear field equation for weak gravity), and is supported by the binary pulsar experiments. For dynamic problems, the linear field equation is independent of, and furthermore incompatible with the Einstein equation. The linear equation, as a first-order approximation, requires the existence of the weak gravitational wave such that it must be bounded in amplitude and be related to the dynamics of the source of radiation. Due to neglecting these crucial physical associations, in addition to inadequate understanding of the equivalence principle, unphysical solutions were mistaken as gravitational waves. It is concluded theoretically that, as Einstein and Rosen suggested, a physical gravitational wave solution for the 1915 equation does not exist. This conclusion is given further supports by analyzing the issue of plane-waves versus exact "wave" solutions. Moreover, the approaches of Damour and Taylor for the radiation of binary pulsars would be valid only if they are as an approximation of the equation of 1995 update. In addition, the update equation shows that the singularity theorems prove only the breaking down of Wheeler-Hawking theories, but not general relativity. It is pointed out that some Lorentz manifolds are among those that actually disagree with known experimental facts.
Key Words: compatibility, dynamic solution, gravitational radiation, principle of causality, plane-wave, Wheeler-Hawking theories
In physics, the existence of a wave is due to the fact, as required by special relativity, that a physical cause must propagate with a finite speed . This implies also that a wave carries energy-momen