Collapsing Wormholes Sustained by Dustlike 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.
Keywords
Cite
@article{arxiv.2011.05099,
title = {Collapsing Wormholes Sustained by Dustlike Matter},
author = {Pavel E. Kashargin and Sergey V. Sushkov},
journal= {arXiv preprint arXiv:2011.05099},
year = {2020}
}