Comments and answers to your questions

Dear Dr. secCNY:

In my previous response to you, I have answered your questions by pointing out the explicit references that you did not read. Now, I would like to give explicit comments to your questions such that you would understand better the issue of the existence of gravitational solution for the Einstein equation of 1915.

1) First, you seemed to confuse the issue of the existence of real gravitational waves and the issue of the existence of gravitation wave solution for the Einstein equation of 1915. You and I believe that there are real gravitational waves. In other words, we have no different on the issue of the existence of real gravitational waves. However, we differ on whether there is gravitational solution for the Einstein equation .
2) Mathematically, it has been proven that time-dependent solutions exist for the Einstein equation of 1915. We are not different on this issue either. However, a mathematical solution of an equation need not be valid in physics. For instance, even in electrodynamics, satisfying the vacuum equation can be insufficient. For instance, the electromagnetic potential solution A0[exp(t - z)2] (A0 is a constant), is invalid in physics. Thus, a solution free of singularities may not be valid.
3) In physics, theorists usually do not prove the existence of a physical solution. Instead, they show that a specific solution is valid in physics. Moreover, if they cannot get an exact solution, they rely on the perturbation approach, which works well for linear equations.
4) An implicit assumption of the perturbation approach is that the exact solution is bounded in amplitude. However, this is not necessary true for the Einstein equation. For instance, there are bounded weak solutions for the static cases, and thus the perturbation approach works. Consequently, the linearized equation is verified and the parameterized post-Newtonian approximation is invented.
5) However, these schemes break down for the dynamic cases. In the references, I have proved that there is no bounded solution for a dynamic case. Moreover, from the principle of causality, a weak solution must exist if a bounded solution exists.
6) Based on the analysis of plane-wave solutions, the existence of an anti-gravity coupling was initially conjectured because Pauli pointed out that an anti-gravity coupling is allowed. This conjecture is confirmed by the Hulse-Taylor binary pulsars experiments.
7) A modification of Einstein equation of 1915 is necessary because there is no dynamic solution. Validity of the modification with an additional source term with an antigravity coupling is confirmed by showing that, for massive sources, the linearized equation (the Maxwell-Newton Approximation) can be derived independent of the Einstein equation.

I hope that these comments would be helpful for you to understand my papers. Any comments and suggestions you may have will be appreciated. Thank you.

Sincerely yours,

C. Y. Lo