Light Speed Invariant Solution and Its Enlightenment of Field Equation of General Relativity

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.