Traversable wormholes in four dimensions (1807.04726v3)

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.

• The paper reveals that quantum-induced negative Casimir energy from massless fermions stabilizes a four-dimensional traversable wormhole configuration.
• It employs a charged, near-extremal black hole setup within the Einstein-Maxwell framework, where a magnetic field generates Landau levels to satisfy energy conditions.
• The findings imply that established physics can yield wormhole solutions without exotic matter, guiding future research in quantum gravity and black hole mechanics.

Traversable Wormholes in Four Dimensions

The paper by Maldacena, Milekhin, and Popov addresses the theoretical construct of traversable wormholes within a four-dimensional spacetime framework. The authors present a novel solution to the Einstein-Maxwell theories augmented with charged, massless fermions, revealing how quantum effects can enable the formation of traversable wormholes without violating known energy conditions. Specifically, the paper explores how a negative Casimir-like energy, arising from the behavior of massless fermions in a magnetic field, allows for a configuration where a wormhole is both feasible and stable under certain conditions.

Summary of Key Findings

The authors consider a long wormhole that avoids causality violations often associated with such structures. Their approach involves a configuration of charged, near-extremal black holes, where the interaction mediated by fermionic fields leads to a traversable bridge. The proposed geometry consists of two entangled black holes, akin to two ends of a wormhole connected through a throat described by an $AdS_2 \times S^2$ metric. Wormhole solutions to the Einstein-Maxwell equations have traditionally encountered issues due to the need for exotic matter with negative energy density. Herein, the negative energy required is sourced from quantum effects—specifically, the Casimir effect associated with massless fermions under the influence of a magnetic field.

Technical Approach and Results

The paper's primary contribution lies in using the Einstein-Maxwell framework with added fermionic fields to achieve quantum-driven traversable solutions. The magnetic field engenders a series of Landau levels, allowing the massless fermions to create a negative energy density, fulfilling the requirements to stabilize the wormhole. This negative energy is a critical feature permitting the wormhole's existence and avoiding causality violations.

Numerically, the solution includes a binding energy of the wormhole relative to two disconnected extremal black holes, characterized by specific charge-dependent equations. Furthermore, the research finds that the gap for excitations within the wormhole is inversely proportional to its length, thus providing a quantitative measure of traversal difficulty.

Implications and Future Directions

The implication of this work is profound, both theoretically and for future developments in theoretical and experimental physics. Primarily, it suggests a framework where exotic solutions like wormholes could manifest within known physics without the need for speculative exotic matter. This work might stimulate further research into quantum gravitational effects, potentially influencing our understanding of black hole mechanics, quantum entanglement, and general covariance in gravity.

The potential future development avenues include exploring alternative configurations of gauge fields or embedding solutions within grand unified frameworks, such as the Standard Model. Moreover, the practical realization of the traversable conditions, while mainly theoretical at this point, could pave the way for experimental horizons, should our technological and observational capabilities advance sufficiently.

Conclusion

The traversable wormhole solution presented in this paper introduces an intriguing interplay between quantum field theory and general relativity, offering new paths for theoretical exploration. The successful modeling of a wormhole without violating causality—via quantum-induced negative Casimir energy—is a testament to the innovative approaches possible within established physical theories. This work not only advances theoretical physics but also bridges conceptually our understanding of spacetime's flexible, dynamic nature when intersected by quantum phenomena.