On General Covariance

If the invariance of light speed is absolutely universal in covariant space rather than contra variant space, the following researches and conclusions on general covariance would be so far as to catch up with very high probabilities and reliabilities. As has been verified, it is. Basically, general covariance is tested controversial after the investigations on gravitational redshift and acceleration. Further inspections on differential geometry indicate the opportunities of inequality of mixed derivatives of bases for the transformations between Riemannian spaces that will then lead to failure of the classical equations of Christoffel symbols, which is one of the reasons that causes controversies on general covariance. In fact, Christoffel symbols and base derivatives both are valid methodologies for analysis in a non-Euclidean space. Measurable experiments on gravitational redshifts and accelerations have been carried out to support the theoretical results. Conclusions have been drawn that light speed keeps general covariance in gravitational fields, but light energy momentum would not, may as well the motions of massive matters in gravitational fields do not perform general covariance thoroughly. Consequently, inferences on kinematics and relativistic release were put into researches, which have got surprising verifications in applications. In the researches on applicable problems of kinematics and relativistic release, the conclusions and inferences have been forcefully verified furtherly. With the ingenious proposition of the concept of gravitational metrics, the so-called geodesic equations have been falsified to be matter’s kinematic equations anymore. The conservativeness of light angular momentum has been discovered in a most surprising form that has help to find out mistakes in traditional methodologies both on the issues of light deflect and radar echo delay. Renovated solutions for light rays as well as massive matters have been carried out that fabulously impact the traditional methodologies on kinematics of trajectory and time delay, and comprehensively interpret the realities. Newtonian ballistic method was put forward to make numerical analyses on close-to-light-speed motions, and the invalidity of that method on light propagation could be seen as another support to the conclusions and inferences. Especially, the forceful falsifications on energy momentum conservativeness carried out in the discussions on the traditional treatment of time delay of close-to-light-speed particles, have thoroughly exposed the essential mistakes in the way of methodologies. Exponent expression of dynamic mass has been carried out to create dynamic equations that prompt more generalized expressions of kinematics, for light ray’s propagation, for massive matters traveling, especially for that thereby, massive matters moving in strong fields, the problem of planet perihelion precession drawn to argue about the only item that the renovated calculations shows controversial to the declared observations. Dynamic models of fluid planet rings were founded to interpret the evolutions of accretions of quasars and active galactic nuclei and the mechanism of relativistic release. The equation of relativistic release was developed after the conclusions and inferences. It is predicted that the peak release of an inflow is at 1.5 of gravitational radius and the peak luminosity of an accretion may locate at the position of 1.33 of gravitational radius. Relativistic frequency shift interprets the mechanism of giant redshift that predict the probability of observational redshift might be up to more than 20.0. The width equations of emission and absorption lines indicate the mechanism and the positions of broad line regions and narrow line regions. It could be imagined that the relativistic emissions and relativistic absorptions with relativistic redshifts would have involved with fantastic mystery of intrinsic structures of matters that we know less.