About the (in)equivalence between holonomic versus non-holonomic theories of gravity

In this paper, we investigate the scenarios in which a holonomic versus a non-holonomic frame description of gravity theories are equivalent. It turns out that classically, the equivalence holds in a way that is independent of the particular dynamics and/or spacetime dimension. This includes general metric-affine dynamics. A global bundle-theoretical investigation is carried out, uncovering the equivalence principle as the culprit. The equivalence holds as long as the equivalence principle holds. This is not something to be expected when non-invertible configurations of the vielbein field are taken into account. In such cases, the gauge-theoretical description of gravity “unsolders” from spacetime, and one has to decide if gravity is spacetime geometry or an internal gauge theory.