This paper discusses three issues (errors) with the general theory of relativity (Schwarzschild space-time). (a) The issue of two physically different interpretations of the gravitational redshift, which are the longitudinal Doppler effect and the transverse Doppler effect. (b) The issue of multiple lengths of a unit measuring rod. (c) The issue of the Schwarzschild surface, which is the event horizon of “reality” (where “reality” indicates reality in the physical theory) and which is also an apparent singularity that is able to be disregarded (on the desk) artificially. Here, new equations are derived by making a new assumption clearly that the space components of “reality” in the Schwarzschild space-time are a three-dimensional Euclidean space in polar coordinates with “ r in the Schwarzschild metric” as the radius. This indicates a new interpretation of the Schwarzschild space-time, and the three issues (errors) are resolved, suggesting that the assumption is correct. The interpretation is made mainly based on the application of the time delay and Lorentz contraction in special relativity theory to a free-fall frame from infinity. Also in Einstein's original paper, “The Foundation of the General Theory of Relativity” A. Einstein, Ann. Phys. 354 , 769 (1916), in the latter half of its §22 (in contradiction with the first half), a space corresponding to a three-dimensional Euclidean space of the radius r (polar coordinates) has been assumed in practice (actually) as space as reality, and a figure based on this assumption has been provided, where correct results such as the curvature of rays have been obtained. At that time, when applying special relativity theory, it is indicated that free-fall frames are not inertial frames because the speed of light is not c = constant in there. The length of the space radius component as “reality” is assumed to be only the length of the radius r . Therefore, the length of the space radius component in the local Lorentz frame instantaneously at rest in the Schwarzschild space-time and the other lengths due to general coordinate transformation are interpreted as mathematical lengths (numerical values) rather than lengths as “reality.” Because the local Lorentz frame is a mathematical existence (which is not “reality”), the laws of physics mathematically hold there. By considering the expression for the (mathematical) energy of a mass point in free fall from infinity in this mathematical local Lorentz frame instantaneously at rest, a new equation for the potential energy in the Schwarzschild space-time has been derived. In Appendix E, in the solar system, we find that for an observer in a free-fall frame from infinity, the oscillation of an arbitrary stationary space point on the radius owing to light coming from the surface of the sun, which is found because of a semi-transparent mirror tilted by 45 ° relative to the radius, is always constant (the same color). This is because the oscillation (period and frequency) of the arbitrary stationary space point on the radius due to the coordinate time is constant (Appendix D). In Subsection 2 of Appendix G, it is explained that the four-dimensional lengths are theoretical (mathematical) rather than real lengths.
Tetsuya Oohata (Tue,) studied this question.