The Precise Inner Solutions of Gravity field Equations of Hollow and Solid Spheres and the Theorem of Singularity

TL;DR

This paper derives exact inner solutions for gravity fields of hollow and solid spheres, showing that singularities and infinite pressures predicted by general relativity are artifacts of the mathematical approach, not physical realities.

Contribution

It demonstrates that singularities and infinite pressures in black holes are due to the mathematical methods of curved space-time, challenging traditional Einsteinian black hole models.

Findings

Singularities cannot exist in the inner solutions of spheres.

Pressure at the center of spheres cannot be infinite.

Black holes predicted by general relativity may not exist in nature.

Abstract

In the present calculation of the inner solution of gravity field equation with spherical symmetry, in order to avoid the singularity appearing in the center of sphere, we actually let the integral constant to be zero. It is proved in this paper that the constant can not be zero. The metric of inner gravity field of hollow sphere is calculated at first. Then let the inner radius of hollow sphere become zero, we obtain the metric of inner gravity field of solid sphere. Based on the definition of energy momentum tensor of general relativity, the gravity masses of hollow and solid spheres in curved space are calculated strictly. The results indicate that no matter what the masses and densities of hollow sphere and solid sphere are, space-time singularities would appear in the centers of spheres. Meanwhile, no matter what the mass and density are, the intensity of pressure at the center point of solid sphere can not be infinite. That is to say, the material can not collapse towards the center of so-called black hole. In stead, it may be that there exist the spherical surfaces of infinite pressure inside the hollow and solid spheres, and material would collapse toward the surfaces so that the common spheres are unsteady. At the center of solid sphere and on its neighboring region, pressure intensities would become negative values. There may be a region for hollow sphere in which pressure intensities would become negative values too. The results only indicate that the singularity black holes predicated by general relativity are caused by the descriptive method of curved space-time and can not exist in nature actually. If black holes exist really in the universe, they can only be the Newtonian black holes, not the Einstein's black holes.