Traversable wormholes in four dimensions

TL;DR

This work constructs a four-dimensional traversable wormhole within Einstein-Maxwell theory by leveraging the negative energy from massless charged fermions occupying the lowest Landau level in a strong magnetic field. The setup effectively joins two near-extremal magnetically charged black holes through an AdS$_2\times$S$^2$ throat whose length $\ell$ is fixed by a balance between classical energy and quantum Casimir contributions, yielding a long-lived, horizon-free wormhole. The solution is metastable and highly sensitive to energy input, but can be stabilized for substantial times via rotation or embedding in AdS$_4$ sectors, and can be embedded in the Standard Model if the throat is small compared to the electroweak scale. The authors further discuss generalizations to multiple fermion flavors, large-$N_f$ limits, and a SM-based embedding with a calculable throat central charge, along with open questions about formation, stability, and potential connections to entanglement and AdS/CFT constructions.

Abstract

We present a wormhole solution in four dimensions. It is a solution of an Einstein Maxwell theory plus charged massless fermions. The fermions give rise to a negative Casimir-like energy, which makes the wormhole possible. It is a long wormhole that does not lead to causality violations in the ambient space. It can be viewed as a pair of entangled near extremal black holes with an interaction term generated by the exchange of fermion fields. The solution can be embedded in the Standard Model by making its overall size small compared to the electroweak scale.

Figures (8)

• Figure 1: Schematic form of the solution we discuss here. It is a traversable wormhole threaded by magnetic fields. This drawing was made by John Wheeler in 1966.
• Figure 2: In (a) we see a particular field line highlighted in green. There is a corresponding lowest Landau level state localized around this field line. It describes a massless two dimensional field moving along the field line, which has the topology of a circle. In (b) we see a cylindrical spacetime. The null line that wraps around the circle is not achronal, since we can see that there are points that are timelike separated along this null line. The average null energy along this line is negative.
• Figure 3: Schematic form of a near extremal black hole geometry. As we approach extremality, a long "throat" with an $AdS_2\times S^2$ geometry develops.
• Figure 4: Magnetic field lines for two sources at distance $d$. We have plotted the magnetic field lines for a few values of $\nu$ in equation (\ref{['MFline']}). We have also defined the angles $\theta_1$, $\theta_2$.
• Figure 5: We separate the solution into three overlapping regions: 1) the wormhole, 2) the mouth and 3) the nearly flat space region. Within each region we describe the solution using a different metric which coincide with that of the next region in the overlapping regions of validity.