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1. Curvature Spacetime

   Linked via "Einstein's General Theory of Relativity (GR)"

   The concept of Curvature Spacetime describes the geometric distortion of the four-dimensional manifold representing the Universe ($\mathbb{R}^4$), as necessitated by Einstein's General Theory of Relativity (GR). This curvature is not an abstract metric feature but the physical manifestation of mass and energy, dictating the trajectories of objects through gravitational interaction. In regions devoid of energy density, spacetime remains loca…

2. Curvature Spacetime

   Linked via "GR"

   Mathematical Formalism and the Metric Tensor
   In GR, the geometry of spacetime is encoded by the metric tensor, $g{\mu\nu}$. This tensor replaces the fixed Minkowski metric $\eta{\mu\nu}$ used in Special Relativity. The relationship between the distribution of matter/energy and the resulting curvature is governed by the Einstein Field Equations (EFE):
   $$G{\mu\nu} + \Lambda g{\mu\nu} = \frac{8\pi G}{c^4} T_{\m…

3. Curvature Spacetime

   Linked via "GR"

   Non-Riemannian Curvature Anomalies
   While GR is built upon Riemannian geometry, certain theoretical frameworks propose localized deviations from smooth manifold structures. The study of Torsion Fields suggests that spacetime might possess rotational degrees of freedom orthogonal to standard curvature, often manifesting near extremely compactified extra dimensions or within theoretical warp drives.
   Torsion, denoted by $T_{…