论文标题
（3+1） - 扭转和非金属的重力形成：应力 - 能量摩托仪方程
(3+1)-Formulation for Gravity with Torsion and Non-Metricity: The Stress-Energy-Momentum Equation
论文作者
论文摘要
我们得出了广义的高斯 - 库达·梅纳迪（GCM）方程，以与扭转和非金属级的一般仿射联系。此外，我们表明，歧管上连接的度量兼容性和无扭转条件遗传到其超曲面的连接。作为这些结果的物理应用，我们为特殊情况的公制f（r） - 重力（f（r）= r（公制的属于度疗法的一般相对论（MAGR））得出（3+1）-Einstein场方程（EFE）。受到几何动力学的概念的促进，由于非变化的扭转和非中型性，我们引入了有关超表面的其他变量。使用这些其他变量，我们表明，对于MAGR，EFE的能量，动量和应力 - 能量部分都是动态的，即，所有这些都包含相对于时间坐标的数量的导数。对于Levi-Civita连接，可以恢复哈密顿量和动量（差异）约束，并获得GR的标准动力学。
We derive the generalized Gauss-Codazzi-Mainardi (GCM) equation for a general affine connection with torsion and non-metricity. Moreover, we show that the metric compatibility and torsionless condition of a connection on a manifold are inherited to the connection of its hypersurface. As a physical application to these results, we derive the (3+1)-Einstein Field Equation (EFE) for a special case of Metric-Affine f(R)-gravity when f(R)=R, the Metric-Affine General Relativity (MAGR). Motivated by the concept of geometrodynamics, we introduce additional variables on the hypersurface as a consequence of non-vanishing torsion and non-metricity. With these additional variables, we show that for MAGR, the energy, momentum, and the stress-energy part of the EFE are dynamical, i.e., all of them contain the derivative of a quantity with respect to the time coordinate. For the Levi-Civita connection, one could recover the Hamiltonian and the momentum (diffeomorphism) constraint, and obtain the standard dynamics of GR.
