A degenerate extension of the Schwarzschild exterior

TL;DR

This paper introduces new vacuum solutions in first order gravity that combine Schwarzschild exterior regions with degenerate tetrad regions, maintaining finite field-strengths and continuous geometry across boundaries.

Contribution

It presents a novel class of solutions with degenerate tetrads in vacuum gravity, extending Schwarzschild geometry with noninvertible phases and continuous fields.

Findings

Field-strength components remain finite everywhere.

Degenerate tetrad regions exhibit nonvanishing torsion.

Solutions connect invertible and noninvertible phases smoothly.

Abstract

We present vacuum spacetime solutions of first order gravity, which are described by the exterior Schwarzschild geometry in one region and by degenerate tetrads in the other. The invertible and noninvertible phases of the tetrad meet at an intermediate boundary across which the components of the metric, affine connection and field-strength are all continuous. Within the degenerate spacetime region, the noninvertibility of the tetrad leads to nonvanishing torsion. In contrast to the Schwarzschild spacetime which is the unique spherically symmetric solution of Einsteinian gravity, all the field-strength components associated with these vacuum geometries remain finite everywhere.