are of a characteristic polynomial that is in form of Fredholm determinant. They can also be obtained using Faddeev–LeVerrier algorithm. Massive gravity in the vierbein language In 4D orthonormal tetrad frame, we have the bases: where the index is for the 3D spatial component of the -non-orthonormal coordinates, and the index is for the 3D spatial components of the -orthonormal ones. The parallel transport requires the spin connection Therefore, the extrinsic curvature, that corresponds to in metric formalism, becomes where is the spatial metric as in the ADM formalism and initial value formulation. If the tetrad conformally transforms as the extrinsic curvature becomes , where from Friedmann equations , and (despite it is controversial), i.e. the extrinsic curvature transforms as . This looks very similar to the matrix or the tensor . The dRGT was developed inspired by applying the previous technique to the 5D DGP model after considering the deconstruction of higher dimensional Kaluza-Klein gravity theories, in which the extra-dimension(s) is/are replaced by series of N lattice sites such that the higher dimensional metric is replaced by a set of interacting metrics that depend only on the 4D components. The presence of a square-root matrix is somewhat awkward and points to an alternative, simpler formulation in terms of vierbeins. Splitting the metrics into vierbeins as and then defining one-forms the ghost-free interaction terms in Hassan-Rosen bigravity theory can be written simply as (up to numerical factors) In terms of vierbeins, rather than metrics, we can therefore see the physical significance of the ghost-free dRGT potential terms quite clearly: they are simply all the different possible combinations of wedge products of the vierbeins of the two metrics. Note that massive gravity in the metric and vierbein formulations are only equivalent if the symmetry condition is satisfied. While this is true for most physical situations, there may be cases, such as when matter couples to both metrics or in multimetric theories with interaction cycles, in which it is not. In these cases the metric and vierbein formulations are distinct physical theories, although each propagates a healthy massive graviton. The novelty in dRGT massive gravity is that it is a theory of gauge invariance under both local Lorentz transformations, from assuming the reference metric equals the Minkowski metric , and diffeomorphism invariance, from the existence of the active curved spacetime . This is shown by rewriting the previously discussed Stueckelberg formalism in