Astrophysics and Space Science

, 306:205 | Cite as

The Gravitational “Plane Waves” of Liu & Zhou and the Nonexistence of Dynamic Solutions for Einstein’s Equation

  • C. Y. Lo
Original Article


Although both the electromagnetic wave and the gravitational wave can be produced approximately from Maxwell-type equations, there are subtle differences in their respective exact equations. Since gravitational wave carries energy-momentum, the exact field equation of a gravitational wave must have a nonzero source term along its path, whereas a field equation for an electromagnetic wave does not. This explains that there is no weak wave solution of Einstein equation. Historically, neither Einstein & Rosen nor the Physical Review was aware that the nonexistence of gravitational wave solutions is due to a violation of the principle of causality. It is pointed out that the criterion of Liu & Zhou on plane-waves is valid since the principle of causality requires the existence of weak limits. However, due to the influence of the popular but unverified assumption of the existence of dynamic solutions, they made careless errors in their calculations and incorrectly concluded that their plane-waves have weak limits. It is shown that “plane-waves” of Liu & Zhou, is actually unbounded in amplitude, and have no weak limit. Therefore, Liu & Zhou provide additional evidence in supporting the nonexistence of dynamic solutions.


Einstein’s equivalence principle Einstein-Minkowski condition Euclidean-like structure Dynamic solution Gravitational radiation Principle of causality Relativistic causality Plane-wave 


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© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • C. Y. Lo
    • 1
  1. 1.Applied and Pure Research InstituteNashuaUSA

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