A systematic examination of the basic theory of general relativity is made, the meaning of coordinates again is emphasized, the confusion caused by unclear meaning of coordinates in the past is corrected, and the expression of the theory is made more accurate. Firstly, the equation of Einstein’s gravitational field is solved in the usual coordinate system, the existence of light speed invariant solution in the spherically symmetric gravitational field is proved, and in the same time, the solution is determined. It turns out that black holes are not an inevitable prediction of general relativity. The more exact formulas for calculating the curvature of light on the surface of the Sun and the precession angle of the orbit of Mercury are given, and the convergence of general relativistic gravity and special relativistic mechanics under the weak field approximation is realized. Finally, it is shown that the coupling coefficient of the gravitational field equation is not unique. Modifying this coefficient is an ideal project to eliminate the singularities of general relativity on the condition keeping the field equation concise and elegant, and moreover, it reveals that dark matter and dark energy are the negative energy field in the matter, the expansion of the universe is the appearance of the gradual formation of galaxies in accordance with fractal rules, not only the space between galaxies is expanding but also the galaxies themselves are also expanding, new matter is continuously generated in the celestial bodies, for the first time, the unity of fractal geometry and cosmic dynamics of general relativity is realized, and the formation and evolution of galaxies are brought into the fractal generation mode. This is a living and vivacious universe in which all aspects are gradually strengthening, in sharp contrast to the dying universe under the current cosmological framework.

中文翻译：

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广义相对论场方程的光速不变解及其启示

对广义相对论的基本理论进行了系统的考察，再次强调了坐标的含义，纠正了过去因坐标含义不清而引起的混乱，使理论的表达更加准确。首先，在常规坐标系下求解爱因斯坦引力场方程，证明了球对称引力场中光速不变解的存在，同时确定了该解。事实证明，黑洞并不是广义相对论的必然预测。给出了用于计算太阳表面的光曲率和水星轨道进动角的更精确公式，在弱场近似下实现了广义相对论引力与特殊相对论力学的收敛。最后，证明了引力场方程的耦合系数不是唯一的。修改该系数是在保持场方程简洁明了的条件下消除广义相对论的理想方案，而且它揭示了暗物质和暗能量是物质中的负能量场，是宇宙膨胀的结果是按照分形规则逐渐形成的星系的出现，不仅星系之间的空间在扩大，而且星系本身也在扩大，新物质在天体中不断产生，这是第一次，实现了分形几何和广义相对论宇宙动力学的统一，并将星系的形成和演化引入了分形生成模式。这是一个活泼而活泼的宇宙，各个方面都在逐步加强，这与当前宇宙学框架下垂死的宇宙形成鲜明对比。