# The Modification of the Oppenheimer and Snyder Collapsing Dust Ball to a Static Ball in Discrete Space-time - General Relativity and Quantum Cosmology

The Modification of the Oppenheimer and Snyder Collapsing Dust Ball to a Static Ball in Discrete Space-time - General Relativity and Quantum Cosmology - Download this document for free, or read online. Document in PDF available to download.

Abstract: Besides the singularity problem, the famous Oppenheimer and Snyder solutionis discovered to be of deficiency in two aspects: the internal Friedmannspace-time does not have the inherent symmetry and cannot connect to theexternal Schwarzschild space-time. So the process of gravitational collapsedescribed by this solution is doubtful. The deficiency, together with thesingularity problem, result from the imperfection of the field theory incontinuous space-time, which is expressed by the infinite precision functiontheory. The space-time structure of the Oppenheimer and Snyder dust ball isfounded to be discrete rather than continuous, and to describe the field theoryin discrete space-time it requires a function theory with finite precision.Based on the i order real number and its equivalence class, which is defined inthe real number field, the infinite precision function theory is extended tothe finite precision function theory. The Einstein field equations areexpressed in the form of finite precision, and then the collapsing dust ballsolution in continuous space-time is modified to a static ball solution indiscrete space-time. It solves all the problems of Oppenheimer and Snydersolution and shows that, with Planck length and Planck time as space-timequantum, a mechanism to resist the gravitational collapse could be obtained bythe discretization of space-time.

Author: ** G. Chen**

Source: https://arxiv.org/