Astrophysical Dynamics and Cosmology (Journal of Mathematical Study, 2021)
First, the essence of a physical theory for a multilevel system is throughcoupling 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 thecoordinate system so that the laws of fluid dynamics and heat conductivity are coupledwith gravitational field equations. Another important ingredient in modeling fluidmotion in astrophysics is to use the momentum density field to replace the velocityfield as the state function of cosmic objects. Second, by applying the new symmetry-breakingmechanism and the new coupled astrophysical dynamics model, we rigorouslyprove a basic theorem on black holes: Assume the validity of the Einstein theoryof general relativity, then black holes are closed, innate and incompressible. Third, weprove a theorem on structure of universes. Assume the Einstein theory of general relativity,and the principle of cosmological principle that the universe is homogeneousand isotropic. Then we show that 1) all universes are bounded, are not originated froma Big-Bang, and are static; and 2) The topological structure of our Universe can onlybe the 3D sphere. Also, thanks to the basic properties of black holes, we show that ourresults on our Universe resolve such fundamental problems as dark matter and darkenergy, redshifts and CMB. Fourth, we discovered that both supernovae explosion and AGN jets, as well as many astronomicalphenomena, are due to combined relativistic, magnetic and thermal effects.The radial temperature gradient causes vertical Bénard convection cells, and the relativisticviscous force (via electromagnetic, the weak and the strong interactions) givesrise to an huge explosive radial force near the Schwarzschild radius, leading e.g. tosupernovae explosion and AGN jets.