Original Article

C.Y.Lo

## Abstract

In 1921, the existence of bounded dynamics solutions was raised by Gullstrand. However, some claimed to have explicit examples. It turns out that the bounded plane-wave of Misner, Thorne and Wheeler is due to calculation errors. Wald claimed the second order term of a wave can be obtained, but failed to have an example. Christodoulou and Klainerman claimed to have constructed a set of bounded dynamic solutions. However, such a construction is actually incomplete. ÂÂÃ‚Â‘t Hooft came up with a bounded time-dependent solution, but without an appropriate source. The fact is that bounded dynamic solutions for the Einstein equation actually do not exist. For the dynamic case, the non-linear Einstein equation and its linearization also cannot have compatible solutions. The existence of a dynamic solution requires an additional gravitational energy-momentum tensor with an antigravity coupling. Thus, the space-time singularity theorems, which require the same sign for couplings, are irrelevant to physics. The positive energy theorem of Schoen and Yau means only for stable solutions because no bounded dynamic solutions satisfy the requirement of asymptotically flat. However, such recognition is crucial to identify the charge-mass interaction. Its experimental verification means that EinsteinÂÂÃ‚Â’s unification between electromagnetism and gravitation is proven valid.