On Contributions of S. T. Yau in Mathematics and Physics Related to General Relativity

Abstract

Due to inadequacy in pure mathematics among physicists, the non-existence of dynamic solutions for the Einstein equation was not recognized. Instead, his field equation was perpetuated. The positive energy theorem of Schoen and Yau also continues such an error. Although Yau may not have made errors in mathematics, their positive energy theorem produced not only just useless but also misleading results in physics. Since the Einstein equation does not have a bounded dynamic solution, the condition of asymptotically flat implies that the case can only be a static solution. Thus, their positive energy theorem actually does not have a meaningful application in physics. Yau failed to see this problem of misleading since he has not attempted to find explicit examples to illustrate their theorem. Moreover, E. Witten made the same mistake in his alternative proof, but that was also cited as an achievement for his Fields Medal in 1990. Concurrently, outstanding mathematical contributions of Yau to the completion of the Poincare conjecture are pointed out. Related issues are also discussed. 04.20.-q, 04.20.