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Bl\'azquez-Salcedo-Knoll-Radu Wormholes Are Not Solutions to the Einstein-Dirac-Maxwell Equations
General Relativity and Quantum Cosmology · Submitted 30 Aug 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Thus, the BSKR wormholes cannot be solutions to the EDM equations.
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The abstract, sentence by sentence
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 $r=0$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recently, Bl\'azquez-Salcedo, Knoll, and Radu (BSKR) have given a class of static, spherically symmetric, traversable wormhole spacetimes with Dirac and Maxwell fields. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | 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 ($r \leq 0$). | background 0.94 | 0.06 | 0.02 | asserted 1.00 |
| s2 | However, it can be seen that the BSKR metric fails to be $C^3$ on the wormhole throat at $r=0$. | result 0.95 | 0.61 | 0.08 | asserted 0.97 |
| s3 | 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. | result 0.83 | 0.85 | 0.08 | asserted 0.98 |
| s4 | Thus, the BSKR wormholes cannot be solutions to the EDM equations. | result 0.99 | 0.86 | 0.96 | asserted 1.00 |
| s5 | 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 $r=0$. | interpretation 0.90 | 0.84 | 0.21 | asserted 1.00 |
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Original 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 $r=0$.
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References
How the literature uses it
6 arXiv papers cite this in 7 sentences
Papers citing it · 3 sentences without a confident label
Contests it 2 papers
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Danielson et al. [ref] it is argued that the wormhole solution presented in [ref] suffers from a failure of the Maxwell and Dirac fields to satisfy the necessary matching conditions.
A note on "Traversable wormholes in Einstein-Dirac-Maxwell theory" · Introduction · contest 0.90
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The original static solutions found in [ref] have some concerning properties [ref] which the asymmetric static solutions found in [ref] avoid.
Einstein-Dirac-Maxwell wormholes in quantum field theory · Introduction · contest 0.77
Cites it as background 2 papers
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Since the present note was written and submitted (April 2021), a few relevant papers have appeared [ref] .
A note on "Traversable wormholes in Einstein-Dirac-Maxwell theory" · Introduction · 0.96
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Quite recently, examples of models were obtained using classical spinor field sources [ref] , which can thus acquire exotic properties.
Field sources for Simpson-Visser space-times · Introduction · 0.84
What it cites · 4 sentences without a confident label
Contests 2 papers
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Similarly, in order for ([ref]) to hold, it is necessary and sufficient that [equation] This condition was not imposed by BSKR [ref] .
Einstein-Dirac-Maxwell wormholes: ansatz, construction and properties of symmetric solutions · Matching Conditions for BSKR Wormholes · contest 0.71
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This fact also can be deduced from the plots given in [ref] for the scalar curvature and the Kretschmann scalar, which can be seen to have a discontinuous derivative at $r=0$.
Traversable wormholes in Einstein-Dirac-Maxwell theory · Smoothness of Solutions at $r=0$ · contest 0.81
Cites as background 1 paper
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The existence of a traversable wormhole would require a violation of the averaged null energy condition [ref] , and such a violation would be of considerable interest in its own right.
Topological Censorship · Introduction · 0.84
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