Matter-free gravitational collapse and the equivalence principle

We investigate the gravitational collapse of a spherically symmetric degenerate wormhole in vacuum, treated as a purely geometric object that is free of matter yet carries a gravitational mass parameter M. Building on the polynomial, g2-regularized form of the Einstein equations, we use the Klinkhamer metric as a concrete example of such a matter-free field source and recall that it reproduces the Schwarzschild exterior on each sheet while remaining an exact vacuum solution, including at the degenerate throat. We then formulate an extended equivalence principle which postulates that this geometric mass plays the role of both gravitational and inertial mass for the wormhole throat, viewed as the single dynamical degree of freedom. Applying this extended principle reduces the field-theoretic problem of radial wormhole dynamics to the motion of a massive test particle in a Schwarzschild spacetime with mass M, for which the collapse trajectory can be obtained analytically. We prove that any bound state of a traversable Klinkhamer wormhole inevitably collapses into a non-traversable Einstein-Rosen wormhole, and we estimate the collapse time, showing that the traversable phase, although non-stationary, can be a long-lived matter-free configuration.