Matter-free gravitational collapse and the equivalence principle

TL;DR

This paper extends the equivalence principle to matter-free gravitational sources, demonstrating that certain wormholes behave like test particles and tend to collapse into nontraversable structures, with implications for their longevity.

Contribution

It proposes an extension of the equivalence principle to matter-free objects and applies it to analyze the dynamics and stability of Klinkhamer wormholes.

Findings

A degenerate wormhole's radial dynamics mimic test particle fall in Schwarzschild field.

Bound Klinkhamer wormholes eventually collapse into Einstein-Rosen wormholes.

Traversable Klinkhamer wormholes can be long-lived despite being nonstationary.

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.