[Paper Review] Conical thin shell wormhole from global monopole: A theoretical construction

Farook Rahaman, Mehedi Kalam+1 more|ArXiv.org|Apr 24, 2008

Spacecraft and Cryogenic Technologies1 references3 citations

TL;DR

This paper constructs a conical thin shell wormhole using a global monopole spacetime via the Darmois-Israel formalism, resulting in a non-asymptotically flat geometry with a deficit solid angle. The study analyzes throat dynamics, linearized stability under radial perturbations, and quantifies the total exotic matter required, showing it can be minimized by tuning the monopole's symmetry-breaking scale and mass, offering a mechanism to reduce energy condition violations in traversable wormhole models.

ABSTRACT

By applying 'Darmois-Israel formalism', we establish a new class of thin shell wormhole in the context of global monopole resulting from the breaking of a global O(3) symmetry. Since global monopole is asymptotically conical (no longer asymptotically flat), we call it as conical thin shell wormhole. Different characteristics of this conical thin shell wormhole, namely, time evolution of the throat, stability, total amount of exotic matter have been discussed.

Motivation & Objective

• To explore the possibility of forming thin-shell wormholes from global monopole spacetimes, which are asymptotically conical rather than asymptotically flat.
• To minimize the amount of exotic matter required to sustain a traversable wormhole, a key challenge in wormhole physics.
• To analyze the dynamical stability of the wormhole throat under linearized radial perturbations.
• To quantify the total exotic matter content using surface integrals in the thin-shell formalism.
• To investigate how parameters like the monopole's symmetry-breaking scale and mass affect the exotic matter requirement and stability.

Proposed method

• Applies the Darmois-Israel formalism to surgically join two global monopole spacetimes along a timelike hypersurface, forming a thin-shell wormhole.
• Uses the Barriola-Vilenkin solution for the global monopole metric, characterized by a deficit solid angle and non-vanishing curvature.
• Derives the energy-momentum tensor on the shell, identifying negative energy density and negative pressure as signatures of exotic matter.
• Performs linearized stability analysis by perturbing the throat radius and deriving a potential function V(a), with stability requiring V''(a₀) > 0.
• Introduces a sound speed parameter β² = ∂p/∂σ to parameterize the equation of state and derive a stability criterion in terms of β₀².
• Computes total exotic matter via surface integrals: Ω₁ = ∫ρ√−g d³x and Ωₜ = ∫(ρ + pₜ)√−g d³x, evaluated at the throat radius a₀.

Experimental results

Research questions

• RQ1 Can a thin-shell wormhole be constructed from a global monopole spacetime, given its conical asymptotic structure?
• RQ2 What is the time evolution of the throat radius under different initial conditions, and does it lead to stable or unstable configurations?
• RQ3 Under what conditions is the thin-shell wormhole dynamically stable against radial perturbations?
• RQ4 How much exotic matter is required to sustain the wormhole, and can this amount be reduced by tuning physical parameters?
• RQ5 How do the symmetry-breaking scale η and monopole mass M influence the total exotic matter content and stability?

Key findings

• The throat radius expands indefinitely if the initial velocity is non-zero, indicating that the wormhole is dynamically unstable unless the initial velocity is exactly zero.
• A static equilibrium solution exists when the initial velocity is zero, corresponding to a constant throat radius.
• Stability is achieved only when the sound speed parameter β₀² satisfies a specific inequality involving the monopole parameters, indicating a restricted region of parameter space for stability.
• The total amount of exotic matter, quantified by Ω₁ and Ωₜ, decreases with increasing symmetry-breaking scale η and increasing monopole mass M.
• Graphical analysis confirms that both increasing η and increasing M lead to a reduction in the required exotic matter, supporting the feasibility of minimizing energy condition violations.
• The exotic matter is confined to the thin shell, with energy conditions satisfied outside the shell, confirming that the violation is localized and consistent with the thin-shell model.