离散时空中的非塌缩的尘埃球解

引进了实数的层次性与离散化，将连续函数理论加以改进和推广为离散函数理论，并基于由离散函数理论所表示的经典广义相对论来讨论尘埃物质的引力塌缩问题，指出了关于这个问题的连续体系的Oppenheimer 和Snyder解中的Friedmann内解与Schwarzschild外解的不完整性并加以拓展和离散化，导出了一种非塌缩的尘埃物质结构，消除了引力奇性并揭示了时空离散化的深刻性质. 关键词： 离散实数 离散时空 广义相对论 Oppenheimer 和Snyder解 奇性自由

A non-collapsing solution of a uniform-density ball of dust in the discrete spacetime

A discrete function theory is found based on the continuous function theory and the discretization of real numbers, which is used to express the classical general relativity and analyse the collapse of a uniform-density ball of dust. It i s shown that the intrinsic and extrinsic geometrices do not actually match at th e join between the Friedmann interior and the Schwarzschild exterior for the Opp enheimer and Snyder solution as a continuum. With the discrete function theory, we can extend and discretize the solution to form a complete non-collapsing solution of the ball of dust, thereby eliminate the gravitational singularity and reveal the deep nature of the discretization of spacetime.