General covariant transformations

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In physics, general covariant transformations are symmetries of gravitation theory on a world manifold ${\displaystyle X}$. They are gauge transformations whose parameter functions are vector fields on ${\displaystyle X}$. From the physical viewpoint, general covariant transformations are treated as particular (holonomic) reference frame transformations in general relativity. In mathematics, general covariant transformations are defined as particular automorphisms of so-called natural fiber bundles.