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1. General Covariance

   Linked via "Kretschmann scalar"

   This tensor nature guarantees covariance. A tensor field transforms predictably under coordinate transformations, ensuring that if the laws are written in terms of these objects, they retain the same structure after relabeling coordinates.
   However, this covariance leads to a curious ontological consequence. Because the metric itself is a dynamical variable subject to coordinate transformations, the notion of a fixed background spacetime is abandoned. This has led some theorists to suggest that the ph…

2. General Covariance

   Linked via "Kretschmann Scalar"

   | :--- | :--- | :--- |
   | Ricci Scalar | $R = g^{\mu\nu} R_{\mu\nu}$ | Tidal stress potential; linked to vacuum energy in certain models. |
   | Kretschmann Scalar | $K = R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta}$ | Measures the intrinsic "lumpiness" of spacetime curvature. |
   | Weyl Tensor Invariant | $C^2 = C_{\alpha\beta\gamma\delta}C^{\alpha\beta\gamma\delta}$ | Related to the propagation speed of gravitational shear waves. |