[Paper Review] Theoretical construction of Morris-Thorne wormholes compatible with quantum field theory

Peter K. F. Kuhfittig|arXiv (Cornell University)|Aug 28, 2009

Black Holes and Theoretical Physics7 references6 citations

TL;DR

This paper proposes a theoretical framework for Morris-Thorne wormholes that are compatible with quantum field theory by minimizing the exotic matter region through strategic fine-tuning of metric coefficients. By balancing the thickness of the exotic region with the degree of fine-tuning and satisfying quantum inequalities and traversability criteria, the model achieves a proper exotic region thickness of approximately 0.1 mm, demonstrating macroscopic viability within quantum constraints.

ABSTRACT

This paper completes and extends some earlier studies by the author to show that Morris-Thorne wormholes are compatible with quantum field theory. The strategy is to strike a balance between reducing the size of the unavoidable exotic region and the degree of fine-tuning of the metric coefficients required to achieve this reduction, while simultaneously satisfying the constraints from quantum field theory. The fine-tuning also serves to satisfy various traversabilty criteria such as tidal constraints and proper distances through the wormhole. The degree of fine-tuning turns out to be a generic feature of the type of wormhole discussed.

Motivation & Objective

• To reconcile Morris-Thorne wormholes with quantum field theory by satisfying quantum inequalities and energy condition constraints.
• To minimize the proper thickness of the exotic matter region around the wormhole throat while keeping fine-tuning of metric coefficients within reasonable bounds.
• To ensure the wormhole satisfies key traversability criteria, including tidal force limits and finite proper distances for travelers.
• To extend and refine earlier models by the author to achieve a balanced trade-off between exotic matter reduction and metric parameter fine-tuning.
• To demonstrate that macroscopic wormholes can exist without violating quantum field theory, even with arbitrarily small exotic regions, by adjusting the redshift function β(r) and shape function b(r).

Proposed method

• Uses a spherically symmetric, static wormhole metric with redshift function β(r) and shape function b(r), where e^{2α(r)} = 1 / (1 - b(r)/r).
• Applies the Einstein field equations in orthonormal frame to derive components of the stress-energy tensor, identifying energy density ρ, radial tension τ, and lateral pressure p.
• Imposes the condition that the weak energy condition (WEC) is violated only within a narrow interval [r₀, r₁], confining exotic matter to a thin band.
• Employs the extended quantum inequality from Ford and Roman to constrain the violation of the null energy condition, ensuring compatibility with quantum field theory.
• Fine-tunes β′(r) and b(r) such that the expression (b(r)/r - b′(r) - 2rβ′(r)(1 - b(r)/r)) is near zero, minimizing the quantum inequality violation.
• Uses the geodesic observer velocity v ≈ 1 to satisfy the quantum inequality bound, ensuring the throat radius r₀ is macroscopic and traversable.

Experimental results

Research questions

• RQ1 Can Morris-Thorne wormholes be constructed such that they are compatible with quantum field theory while minimizing the exotic matter region?
• RQ2 What is the minimal proper thickness of the exotic region that still satisfies quantum inequalities and traversability constraints?
• RQ3 How does fine-tuning of β′(r) and b(r) affect the balance between exotic matter reduction and physical feasibility?
• RQ4 To what extent can the exotic region be reduced without violating quantum energy conditions or making the required parameter tuning impractical?
• RQ5 Can the throat radius r₀ be macroscopic while maintaining compatibility with quantum field theory and observer traversability?

Key findings

• The exotic region's proper thickness is minimized to approximately 0.1 mm, significantly reducing the volume of exotic matter required.
• The model satisfies the extended quantum inequality from Ford and Roman, ensuring compatibility with quantum field theory across the entire spacetime.
• The degree of fine-tuning required is deemed reasonable and generic for this class of wormhole, avoiding unphysical parameter choices.
• The radial velocity of a geodesic observer approaches 1 near the throat, ensuring the quantum inequality constraint is satisfied with a vanishingly small denominator.
• The throat radius r₀ is macroscopic (included in rₘ), making the wormhole traversable for humanoid travelers under tidal and distance constraints.
• The analysis confirms that decreasing the coordinate distance can reduce the exotic region thickness indefinitely, though at the cost of increasing fine-tuning beyond practical limits.