Self-accelerating Massive Gravity: How Zweibeins Walk through
  Determinant Singularities
  The theory of massive gravity possesses ambiguities when the spacetime metric
evolves far from the non-dynamical fiducial metric used to define it. We
explicitly construct a spherically symmetric example case where the metric
evolves to a coordinate-independent determinant singularity which does not
exist in the initial conditions. Both the metric and the vierbein formulation
of the theory are ill-defined at this point. In unitary gauge, the chart of the
spacetime ends at this point and does not cover the full spacetime whereas the
spherically symmetric vierbeins, or zweibeins, of the fiducial metric become
non-invertible and do not describe a valid metric. Nonetheless it is possible
to continuously join a zweibein solution on the other side of the singularity
which picks one of the degenerate solutions of the metric square root. This
continuous solution is not the choice conventionally made in the previous
literature. We also show that the Stueckelberg equations of motion on the
self-accelerating branch prevent solutions from evolving to a more pathological
situation in which the spacetime vierbeins lack a crucial symmetry with the
fiducial vierbeins and real square roots fail to exist.
