The Non-linear Einstein Equation and Conditional Validity of its Linearization

C. Y. Lo

Applied and Pure Research Institute

 7 Taggart Drive, Unit E, Nashua, NH 03060

Abstract

It is shown through explicit calculations to illustrate that, for the dynamic case, the non-linear Einstein equation and its linearized equation have no compatible solutions. Thus, for the dynamic cases, the Einstein equation and its “linearization” are independent equations, and the “linearization” procedure is not valid. In fact, the linearized equation is compatible with a 1995 modified Einstein equation that added a gravitational energy-stress tensor with an anti-gravity coupling in the source. This makes clear that there is no bounded dynamic solution for the Einstein equation as Gullstrand suspected because the gravitational energy-stress tensor is not in its source. All these are crucial to show that Einstein’s conjecture of unification is correct.

KEYWORDS: dynamic solution; gravitational radiation; principle of causality;

PACS: 04.20.Cv; 04.50.-h; 04.50.Kd; 04.80.Cc

“Unthinking respect for authority is the greatest enemy of truth.” – A. Einstein