Mathematical Principles of Theoretical Physics

1.9 The Universe

3.Geometric realization of a black hole.As described in Section 4.1 in (Ma and Wang,
2014a) and in Section7.3.1, the geometrical realization of a black hole, dictated by the
Schwarzschild and TOV metrics, clearly manifests that the real world in the black hole is
a hemisphere with radiusRsembedded inR^4 , and at the singularityr=Rs, the tangent space
of the black hole is perpendicular to the coordinate spaceR^3.
This geometric realization clearly demonstrates that the disk in the realization spaceR^3
is equivalent to the real world in the black hole. If the outside observer observes that nothing
gets inside the black hole, then nothing will get inside the black hole in the reality as well.

1.9 The Universe

7.3.4 Origin of stars and galaxies.

Modern cosmology adopts the view that our Universe is formedthrough the Big-Bang
or Big-Bounce; see among others (Harrison, 2000 ;Kutner, 2003 ;Popławski, 2012 ;Roos,
2003 ). Based on our new insights on black holes, we have reached very different conclusions
on the structure and formation of our Universe.
It is clear that the large scale structure of our Universe is essentially dictated by the law
of gravity, which is based on Einstein’s two principles: theprinciple of general relativity
and the principle of equivalence, as addressed in Section1.1. Also, strong cosmological
observational evidence suggests that the large scale Universe obey the cosmological principle
that the Universe is homogeneous and isotropic.

Basic assumptions

(a) the Einstein theory of general relativity, and

(b) the cosmological principle.

With Assumption (a) above, we have our blackhole theorem, Theorem7.15, at our dis-
posal. Then we can draw a number of important conclusions on the structure of our Universe.

1. LetEandMbe the total energy and mass of the Universe:

(1.9.1) E=kinetic+electromagnetic+thermal+Ψ, M=E/c^2 ,

whereΨis the energy of all interaction fields. The total massMdictates the Schwarzschild
radiusRs.
If our Universe were born to the Big-Bang, assuming at the initial stage, all energy is
concentrated in a ball with radiusR 0 <Rs, by the theory of black holes, then the energy
contained inBR 0 must generate a black hole inR^3 with fixed radiusRsas defined by (1.8.2).
If we assume that at certain stage, the Universe were contained in ball of a radiusRwith
R 0 <R<Rs, then we can prove that the Universe must contain a sub-blackhole with radius
rgiven by

r=

√

R

Rs

R.

Based on this property, the expansion of the Universe, with increasingRtoRs, will give rise to
an infinite sequence of black holes with one embedded to another. Apparently, this scenario