Emergency of black holes from wormholes

TL;DR

This paper explores a spherically symmetric Dirac star model with a phantom field, revealing that small wormholes can mimic black holes, with the solution's properties differing significantly from trivial spacetime cases.

Contribution

It introduces a novel wormhole solution in a Dirac star model with phantom fields, highlighting the emergence of black hole-like behavior near small wormhole throats.

Findings

Wormhole solutions exhibit asymmetry in fields and metrics.

Small wormholes can approximate black hole solutions.

Near the throat, the Kretschmann scalar diverges, indicating untraversability.

Abstract

In this paper, we study the spherically symmetric Dirac star model in the presence of a phantom field, obtaining a traversable wormhole solution in non-trivial topological spacetime. This solution exhibits asymmetry in both the field configuration and the metric and possesses a finite ADM mass $M$ and Noether charge $Q$. Furthermore, we find that due to the presence of a wormhole at the center, this solution exhibits many differences from the Dirac star under trivial spacetime. Notably, when the wormhole throat size is small, our numerical calculations indicate the emergence of an extremely approximate black hole solution on one side of the wormhole spacetime, a phenomenon unexplored. At this time, the Kretschmann scalar near the throat tends to infinity, indicating the wormhole becomes untraversable.