Matter-free gravitational collapse and the equivalence principle
Abstract
The dynamics of a degenerate spherically symmetric wormhole in a vacuum is considered. An extension of the equivalence principle to matter free objects that are the source of a gravitational field is proposed. Using the Klinkhamer metric as an example, it is shown that a degenerate wormhole is precisely such an object. Application of the extended equivalence principle reduces the radial dynamics of the Klinkhamer wormhole to the dynamics of the radial fall of a test particle in a Schwarzschild gravitational field. It is proven that any bound state of the traversable Klinkhamer wormhole eventually collapses into a nontraversable Einstein-Rosen wormhole. An estimate is presented showing that the traversable Klinkhamer wormhole, although nonstationary, is a longlived state.
Cite
@article{arxiv.2512.16933,
title = {Matter-free gravitational collapse and the equivalence principle},
author = {Juri Dimaschko},
journal= {arXiv preprint arXiv:2512.16933},
year = {2026}
}