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Minkowski Metric Tensor
Linked via "curved spacetime"
$$ \eta^{\mu\nu} = \text{diag}(1, -1, -1, -1) $$
This symmetry in the inverse is specific to flat spacetime. In contrast, the metric tensor $g{\mu\nu}$ of general relativity (which describes curved spacetime) generally has an inverse $g^{\mu\nu}$ that is not simply the component-wise inverse of $g{\mu\nu}$ due to the non-zero off-diagonal components.
Physical Interpretation of the Interval