n disagreement with experiments [9,10]. Their invalid acceptance is due to the incorrect belief3) that the equivalence principle were satisfied by any Lorentz manifold [11].
Moreover, Einstein's notion cannot be exact, since it is not localizable [12]. In a field theory, a central problem is the exchange of energy between a particle and the field where the particle is located [13]. Therefore, the gravitational energy-stress must be a tensor (see also Section 4).

2. The Gravitational Wave and Nonexistence of Dynamic Solutions for Einstein's Equation
First, a major problem is a mathematical error on the relationship between (1) and its "linearization". It was incorrectly believed that the linear Maxwell-Newton Approximation [13]

( c(c(( = - K T(m) (( , where (( = ((( - (((((cd(cd) (3a)
and
(((xi, t) = - (T(((yi, (t - R)]d3y, where R2 =(xi - yi)2 . (3b)

always provides the first-order approximation for equation (1). This belief was verified for the static case only.
For a dynamic4) case, however, this is no longer valid. While the Cauchy data can be arbitrary for (3a), but not for (1). The Cauchy data of (1) must satisfy four constraint equations, G(t = -KT(m)(t (( = x, y, z, t) since G(t contains only first-order time derivatives [8]. This shows that (3a) would be dynamically incompatible5) with equation (1) [10]. Further analysis shows that, in terms of both theory [11] and experiments [13], this mathematical incompatibility is in favor of (3), instead of (1).
In 1957, Fock [14] pointed out that, in harmonic coordinates, there are divergent logarithmic deviations from expected linearized behavior of the radiation. This was interpreted to mean merely that the contribution of the complicated nonlinear terms in the Einstein equation cannot be dealt with satisfactorily following this method and that other approach is needed. Subsequently, vacuum solutions that do not involve logarithmic deviation, were founded by Bondi, Pirani & Robinson [15] in 1959. Thus, the incorrect interpretation appears to be justified and the faith on the dynamic solutions maintained. It was not recognized until 1995 [13] that such a symptom of divergence actually shows the absence of bounded physical dynamic solutions.
In physics, the amplitude of a wave is generally related to its energy density and its source. Equation (3) shows that a gravitational wave is bounded and is related to the dynamic of the source. These are useful to prove that (3), as the first-order approximation for a dynamic problem, is incompatible with equation (1). Its existing "wave" solutions are unbounded and therefore cannot be associated with a dynamic source [11]. In other words, there is no evidence for the existence of a physical dynamic solution.
With the Hulse-Taylor binary pulsar experiment [16], it became easier to identify that the problem is in (1). Subsequently, it has been shown that (3), as a first-order approximation, can be derived from physical requirements which lead to general relativity [11]. Thus, (3) is on solid theoretical ground and general relativity remains a viable theory. Note, however, that the proof of the nonexistence of bounded dynamic solutions for (1) is essentially independent of the experimental supports for (3).
To prove this, it is sufficient to consider weak gravity since a physical solution must be compatible with Einstein's [2] notion of weak gravity (i.e., if there were a dynamic solution for a field equation, it should have a dynamic solution for a related weak gravity [11]). To calculate the radiation, consider further,

G(( ( G(1)(( + G(2)(( , where G(1)(( = (c(c(( + H(1)((, (2b)

H(1)(( ( -(c((((c + (((c( + ((((c(dcd , and ?(((? << 1. (2c)

G(2)(( is at least of second order in terms of the metric elements. For an isolated system located near the origin of the space coordinate system, G(2)(t at large r (= (x2 + y2 + z2 (1/2) is of O(K2/r2) (5,8,17(.
One may obtain some general characteristics of a dynamic solution for an isolated system as follows:
1) The c

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