Stellar matter distribution with scale-invariant hierarchical structuring

Abstract

It is generally known that Einstein ́s general relativistic field equations (see Einstein,1915,1917, or later presented in books e.g. by Rindler, 1977, or Tolman, 1987)1,2 describe the 4-dim space time geometry through the gravitational geometry source, i.e. through the cosmic energy-momentum tensor Tik .Oppositely to what is commonly thought, this source tensor is not an easy-to-handle quantity, since the tensor ingredients are dependent on cosmic time in a non-trivial, but fairly complicated, and in a physically not evident or straightforward way. Even though all cosmological models start from the basis of the cosmological principle requiring that the universe at identical cosmic times looks the same from all space points in the universe, this does not make it evident what that means in terms of these Tik -tensor-ingredient data, even not in such a homogeneous and isotropic universe. In case the matter content of the universe can be described as a homogeneously distributed baryonic gas, then the mass density and the scalar pressure of this gas may count as spaceaveraged quantities, but in later, closer to the present phases of the universe, when matter is structured in stars, galaxies and galaxy clusters what in replace of these former quantities should be used then? In terms of gravity sources baryons imprisoned in the body of a star are not like the same number of baryons freely distributed as a cosmic baryon gas. Stellar baryons are much hotter and in the stellar interiors their pressure may strongly count in terms of Tik -ingredients. So the question arises how to make spatially averaged quantities out of them under such conditions.