Degenerate extension of positive and negative mass Schwarzschild geometry

We define a smooth extension of the Schwarzschild exterior geometry, with the spe- cial property that the curvature two-form field is finite everywhere. This spacetime is a solution to the first order field equations in vacuum by construction. Unlike the Kruskal- Szekeres construction based on invertible metrics in the Einsteinian theory, it exhibits a vanishing metric determinant phase over an extended region. The invertible and non- invertible phases of the tetrad meet at an intermediate hypersurface across which the components of the gauge-covariant fields are all continuous. These solutions could be particularly relevant in the study of singularities in general relativity as well as in the context of information loss problem. We also demonstrate that it is not possible to define a similar extension for the case of a negative mass Schwarzschild solution. This is consistent with the general expectation that degenerate metric spacetimes constructed within the Hilbert-Palatini Lagrangian framework should satisfy the energy conditions.