Bl\'azquez-Salcedo-Knoll-Radu Wormholes Are Not Solutions to the Einstein-Dirac-Maxwell Equations

TL;DR

This paper demonstrates that the previously proposed Blázquez-Salcedo-Knoll-Radu wormholes cannot be solutions to the Einstein-Dirac-Maxwell equations due to non-smoothness at the wormhole throat, indicating the presence of unphysical matter sources.

Contribution

It proves that the BSKR wormholes are not genuine solutions to the EDM equations because of their non-smooth matching at the throat, clarifying the nature of their fields.

Findings

BSKR wormholes are not solutions to the EDM equations.

Non-smoothness at the throat implies unphysical matter sources.

Fields would be smooth if matching conditions were properly satisfied.

Abstract

Recently, Bl\'azquez-Salcedo, Knoll, and Radu (BSKR) have given a class of static, spherically symmetric, traversable wormhole spacetimes with Dirac and Maxwell fields. The BSKR wormholes are obtained by joining a classical solution to the Einstein-Dirac-Maxwell (EDM) equations on the "up" side of the wormhole ($r \geq 0$) to a corresponding solution on the "down" side of the wormhole ($r \leq 0$). However, it can be seen that the BSKR metric fails to be $C^3$ on the wormhole throat at $r=0$. We prove that if the matching were done in such a way that the resulting spacetime metric, Dirac field, and Maxwell field composed a solution to the EDM equations in a neighborhood of $r=0$, then all of the fields would be smooth at $r=0$ in a suitable gauge. Thus, the BSKR wormholes cannot be solutions to the EDM equations. The failure of the BSKR wormholes to solve the EDM equations arises both from the failure of the Maxwell field to satisfy the required matching conditions (which implies the presence of an additional shell of charged matter at $r=0$) and, more significantly, from the failure of the Dirac field to satisfy required matching conditions (which implies the presence of a spurious source term for the Dirac field at $r=0$.