Traversable wormholes in Einstein-Dirac-Maxwell theory (2010.07317v2)

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.

• The paper demonstrates traversable wormhole solutions that avoid exotic matter by employing fermionic matter and electric charge.
• It establishes quantitative relations, including a Smarr-like condition with Qₑ/M > 1, that underline the unique features of these configurations.
• Both numerical and exact analytical methods are used to reveal smooth, symmetric wormhole geometries that open new avenues in semiclassical wormhole physics.

Traversable Wormholes in Einstein-Dirac-Maxwell Theory

In the paper of theoretical physics, the concept of traversable wormholes holds a significant position in the exploration of spacetime structures. This paper presents a detailed examination of traversable wormhole solutions within the framework of Einstein-Dirac-Maxwell (EDM) theory, without resorting to exotic matter typically required in such configurations. The authors, Jose Luis Blázquez-Salcedo, Christian Knoll, and Eugen Radu, have constructed a specific example using two massive fermions in a singlet spinor state that showcases spherically symmetric, asymptotically flat configurations devoid of singularities.

Key Findings and Numerical Results

The research highlights several notable aspects of the wormhole solutions in EDM theory:

1. Absence of Exotic Matter: Unlike traditional wormhole models requiring matter that violates the null energy condition and utilizes non-standard Lagrangians, these solutions circumvent such necessities. Utilizing fermionic matter described by quantum wave functions, the team successfully integrates electric charge to achieve smooth geometries with no additional exotic matter at the throat.
2. Quantitative Relations: The solutions exhibit a Smarr relation analogous to that connecting mass and charge in extremal Reissner-Nordström black holes. Specifically, configurations maintain a mass $M$ and electric charge $Q_e$ with the condition $Q_e/M>1$, highlighting a distinctive feature compared to conventional models.
3. Exact Solutions and Symmetric Wormholes: For specific parameter values (massless fermions and ungauged scenarios), the paper reports exact analytical solutions. These configurations show a regular, traversable wormhole nature and confirm the consistency of their framework.
4. Numerical Analysis: Through a comprehensive numerical approach, the authors provide a spectrum of "smooth" solutions characterized by symmetrical wormhole configurations. The investigation covers varied fermion masses and coupling constants, with solutions generally adhering to the condition $q/\mu < 1$.

Implications and Speculations

The paper's findings extend the theoretical foundation of wormholes by presenting a plausible realization within the standard EDM theory, heavily relying on fermionic matter configurations. This pivotal shift has potential implications for understanding geometrodynamics and the role of fermions in astrophysical phenomena:

• Astrophysical Connections: The formalism introduces a unified description that bridges wormhole structures with electromagnetic properties and fermionic interactions. Considering the non-gravitational aspect, these models may have implications for investigating cosmic phenomena and could contribute to the astrophysical search for wormholes.
• Entanglement and Quantum Considerations: The entanglement between fermionic states observed in symmetric configurations aligns with concepts in quantum field theory. Although approached semi-classically, the implications for quantum mechanics and field interactions warrant further exploration.
• Future Research Directions: The acknowledgment of a semiclassical model calls for a deeper investigation into quantum corrections, especially in a quantized matter context. The development of models encompassing the entire spectrum of Standard Model particles and spinor fields remains an open area of exploration.

Overall, this work spearheads a renewed approach in wormhole physics by demonstrating the viability of traversable solutions within classical frameworks, utilizing standard matter constructs. With further exploration and refinement, these insights could catalyze advances in theoretical physics and cosmology.