Collapsing Wormholes Sustained by Dustlike Matter

TL;DR

This paper constructs a dynamic, collapsing dust wormhole in general relativity using Tolman's solution, showing such wormholes can exist without exotic matter but only in non-static, collapsing scenarios.

Contribution

It introduces a novel dynamic wormhole solution supported by dust-like matter, expanding understanding of wormhole configurations beyond static, exotic matter models.

Findings

The dust wormhole collapses under gravity, forming a black hole.

The solution satisfies usual energy conditions during collapse.

It demonstrates non-static wormholes can be supported by normal matter.

Abstract

It is well known that static wormhole configurations in general relativity (GR) are possible only if matter threading the wormhole throat is "exotic"---i.e., violates a number of energy conditions. For this reason, it is impossible to construct {static} wormholes supported only by dust-like matter which satisfies all usual energy conditions. However, this is not the case for non-static configurations. In 1934, Tolman found a general solution describing the evolution of a spherical dust shell in GR. In this particular case, Tolman's solution describes the collapsing dust ball; the inner space--time structure of the ball corresponds to the Friedmann universe filled by a dust. In the present work we use the general Tolman's solution in order to construct a dynamic spherically symmetric wormhole solution in GR with dust-like matter. The solution constructed represents the collapsing dust ball with the inner wormhole space--time structure. It is worth noting that, with the dust-like matter, the ball is made of satisfies the usual energy conditions and cannot prevent the collapse. We discuss in detail the properties of the collapsing dust wormhole.