(untitled) (Journal of Mathematical Study, 2021)
First, the essence of a physical theory for a multilevel system is through coupling different physical laws in different levels by a symmetry-breaking principle, rather than through a unification using larger symmetry. In astrophysical dynamics, the symmetry-breaking mechanism and the coupling are achieved by prescribing the coordinate system so that the laws of fluid dynamics and heat conductivity are coupled with gravitational field equations. Another important ingredient in modeling fluid motion in astrophysics is to use the momentum density field to replace the velocity field as the state function of cosmic objects. Second, by applying the new symmetry-breaking mechanism and the new coupled astrophysical dynamics model, we rigorously prove a basic theorem on black holes: Assume the validity of the Einstein theory of general relativity, then black holes are closed, innate and incompressible. Third, we prove a theorem on structure of universes. Assume the Einstein theory of general relativity, and the principle of cosmological principle that the universe is homogeneous and isotropic. Then we show that 1) all universes are bounded, are not originated from a Big-Bang, and are static; and 2) The topological structure of our Universe can only be the 3D sphere. Also, thanks to the basic properties of black holes, we show that our results on our Universe resolve such fundamental problems as dark matter and dark energy, redshifts and CMB. Fourth, we discovered that both supernovae explosion and AGN jets, as well as many astronomical phenomena, are due to combined relativistic, magnetic and thermal effects. The radial temperature gradient causes vertical Bénard convection cells, and the relativistic viscous force (via electromagnetic, the weak and the strong interactions) gives rise to an huge explosive radial force near the Schwarzschild radius, leading e.g. to supernovae explosion and AGN jets.