This paper derives the elements of classical Einstein–Cartan theory (EC) from classical general relativity (GR) in two ways. (I) Derive discrete versions of torsion (translational holonomy) and the spin-torsion field equation of EC from one Kerr solution in GR. (II) Derive the field equations of EC as the continuum limit of a distribution of many Kerr masses in classical GR. The convergence computations employ “epsilon-delta” arguments, and are not as rigorous as convergence in Sobolev norm. Inequality constraints needed for convergence restrict the limits from continuing to an infinitesimal length scale. EC enables modeling exchange of intrinsic and orbital angular momentum, which GR cannot do. Derivation of EC from GR strengthens the case for EC and for new physics derived from EC.

中文翻译：

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从广义相对论推导爱因斯坦-嘉当理论

本文从经典广义相对论 (GR) 中以两种方式推导出经典爱因斯坦-嘉当理论 (EC) 的要素。(I) 从 GR 中的一个 Kerr 解导出离散版本的扭转（平移完整）和 EC 的自旋扭转场方程。(II) 导出EC的场方程作为经典GR中许多克尔质量分布的连续极限。收敛计算采用“epsilon-delta”参数，并不像 Sobolev 范数中的收敛那么严格。收敛所需的不等式约束将限制限制在无限小的长度范围内。EC 能够模拟内在和轨道角动量的交换，这是 GR 无法做到的。从 GR 派生 EC 加强了 EC 和从 EC 派生的新物理学的情况。