  We present a smooth extension of the Schwarzschild exterior geometry, where
the singular interior is superceded by a vacuum phase with vanishing metric
determinant. Unlike the Kruskal-Szekeres continuation, this solution to the
first-order field equations in vacuum has no singularity in the curvature
two-form fields, no horizon and no global time. The underlying non-analytic
structure provides a distinct geometric realization of `mass' in classical
gravity. We also find that the negative mass Schwarzschild solution does not
admit a similar extension within the first-order theory. This is consistent
with the general expectation that degenerate metric solutions associated with
the Hilbert-Palatini Lagrangian formulation should satisfy the energy
conditions.
