Traversable wormholes in Einstein-Dirac-Maxwell theory

TL;DR

This paper constructs explicit traversable wormhole solutions within Einstein-Dirac-Maxwell theory, demonstrating they can exist without exotic matter and are connected to extremal Reissner-Nordström black holes, with some solutions having a finite mass and charge.

Contribution

It provides the first explicit examples of traversable wormholes in Einstein-Dirac-Maxwell theory without exotic matter, including a massless fermion case.

Findings

Existence of spherically symmetric, asymptotically flat wormhole solutions.

Solutions have finite mass and electric charge with Q_e/M > 1.

Some solutions are connected to extremal Reissner-Nordström black holes.

Abstract

We construct a specific example of a class of traversable wormholes in Einstein-Dirac-Maxwell theory in four spacetime dimensions, without needing any form of exotic matter. Restricting to a model with two massive fermions in a singlet spinor state, we show the existence of spherically symmetric asymptotically flat configurations which are free of singularities, representing localized states. These solutions satisfy a generalized Smarr relation, being connected with the extremal Reissner-Nordstr\"om black holes. They also possess a finite mass $M$ and electric charge $Q_e$, with $Q_e/M>1$. An exact wormhole solution with ungauged, massless fermions is also reported.