Gravitation, Density, Black Holes and Spatial Quantization

Abstract

Making use of Newton’s classical shell theorem, the Schwarzschild metric is modified. This removes the singularity at r = 0 for a standard object (not a black hole). It is demonstrated how general relativity evidently leads to quantization of space-time. Both classical and quantum mechanical limits on density give the same result. Based on Planck’s length and the assumption that density must have an upper limit, we conclude that the lower limit of the classical gravitation theory by Einstein is related to the Planck length, which is a quantum phenomenon posed by dimensional analysis of the universal constants. The Ricci tensor is considered under extreme densities (where Kretschmann invariant = 0) and a solution is considered for both outside and inside the object. Therefore, classical relativity and the relationship between the universal constants lead to quantization of space. A gedanken experiment of light passing through an extremely dense object is considered, which will allow for evaluation of the theory.