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Volume 12: Pages 508-526, 1999
Compatibility with Einstein's Notion of Weak Gravity: Einstein's Equivalence Principle and the Absence of Dynamic Solutions for the 1915 Einstein Equation
C. Y. Lo
Applied and Pure Research Institute, 17 Newcastle Dr., Nashua, New Hampshire 03060 U.S.A.
The basic assumption of Einstein's radiation formula is Einstein's notion of weak gravity, which is supported by the Maxwell‐Newton approximation. This linear field equation is derived from the equivalence principle and concurrently the Einstein equation is obtained. However, compatibility with Einstein's notion of weak gravity, as a physical requirement, originates from the principle of causality. It is shown also that the physical space‐time metric is the normalized metric obtained from the original metric by removing the compensative factors making the variables have units of length. Einstein suggested that any Gaussian coordinate system can be a space‐time coordinate system. An incorrect implicit assumption is that a Lorentz manifold is always diffeomorphic to a physical space. It is proven, as shown through examples, that the equivalence principle necessarily restricts the space‐time coordinate systems, i.e., unrestricted covariance is invalid in physics. Such a restriction implies that the normalized metric is bounded although the original metric may appear to be unbounded. Thus, compatibility with Einstein's notion of weak gravity is a requirement in general relativity. This implies, however, that there is no plane‐wave solution for Einstein's equation of 1915. This fact, and that all known “wave” solutions are unbounded and incompatible with the notion of weak gravity, further confirms that the 1915 equation has no dynamic solution related to radiation.
Keywords: compatibility with Einstein's notion of weak gravity, the equivalence principle, restricted covariance, intrinsically unphysical Lorentz manifold, boundedness, normalized metric, gravitational plane wave, absence of dynamic solution
Received: May 12, 1999; Published online: December 15, 2008