Stability regions of glued wormholes with massless Kim-Lee backreacted spacetimes as interior

Abstract: Asymptotic zero Arnowitt-Deser-Misner (ADM) mass wormholes, such as the zero-mass traversable Ellis-Bronnikov wormhole, are of great interest for astrophysical applications such as in the galactic microlensing. However, when considered individually, they are unstable to small perturbations. On the other hand, there is a possibility that they can be stable as an interior partner of a traversable glued wormhole obtained by suitably gluing the interior to the observationally relevant massive exterior spacetimes across spherically symmetric thin shells. Although the exterior spacetime has non-zero ADM mass, massless interior partner remains massless sharing the stability of the glued wormhole. The dynamics of the thin-shell then demarcates the stability regions of the glued wormhole that we wish to study here by employing the novel concepts of thin-shell "mass" and of "external force" constraints discovered by Garcia, Lobo and Visser. We shall consider two classes, where the zero ADM mass interior are Kim-Lee wormholes glued to the exterior Schwarzschild vacuum and Reissner-Nordström spacetime respectively. It turns out that the stability regions in both cases are almost similar although the two interior Kim-Lee spacetimes are physically very different, one scalar charged and the other electrically charged. The conditions under which the stability of glued wormholes could be achieved are analyzed in detail.

• The paper introduces a novel construction of thin-shell wormholes by gluing massless KL wormholes as interior metrics to classical exterior geometries.
• It employs the GLV formalism to derive stability conditions based on the second derivative of the mass function and external force constraints.
• Results reveal that increased interior charge generally destabilizes the configuration, while a higher exterior charge can enhance stability under certain conditions.

Stability Analysis of Glued Wormholes with Massless Kim-Lee Backreacted Spacetimes as Interior

Introduction

This work investigates the linear stability of thin-shell wormholes constructed by gluing an interior spacetime described by the massless Kim-Lee (KL) backreacted wormhole solution to an exterior vacuum solution, specifically Schwarzschild or Reissner-Nordström (RN) geometries, via a spherically symmetric timelike thin shell. The novelty arises from employing KL wormholes, which are themselves massless but possess nontrivial scalar or electric charges, as interior metrics—a class distinct from the more commonly studied Ellis-Bronnikov wormholes. The analysis focuses on identifying regions of linear stability under spherically symmetric perturbations, using the formalism of Garcia, Lobo, and Visser (GLV), which incorporates both "mass" and "external force" constraints on the shell dynamics.

Massless Kim-Lee Backreacted Wormhole Spacetimes

Scalar-Charged Case

The massless scalar-charged KL wormhole solution is characterized by a metric in the Morris-Thorne form with redshift function $\Phi(r) = 0$ and shape function $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$. Upon choosing $\beta = -1$, the metric simplifies to

$$ds^2 = -dt^2 + \left(1 - \frac{b_0^2 - \alpha}{r^2}\right)^{-1} dr^2 + r^2(d\theta^2 + \sin^2\theta\, d\phi^2),$$

where $\alpha$ is the scalar charge parameter. The wormhole throat is located at $r_{\rm th} = \sqrt{b_0^2 - \alpha}$, and the solution exhibits zero ADM mass in the asymptotic region. This metric reduces to the Ellis-Bronnikov form for $\alpha = 0$.

Electrically-Charged Case

For the electrically charged variant, the metric reads

$$ds^2 = -\left(1 + \frac{Q^2}{r^2}\right) dt^2 + \left(1 - \frac{b_0^2}{r^2} + \frac{Q^2}{r^2}\right)^{-1} dr^2 + r^2(d\theta^2 + \sin^2\theta\, d\phi^2),$$

where $Q$ is the electric charge, satisfying $Q^2 < b_0^2$ for regular throats. The throat radius is $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$0, and the ADM mass remains zero. When $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$1, this metric reduces to the non-massive RN geometry.

Thin-Shell Wormhole Construction and GLV Formalism

Employing the cut-and-paste method, two spacetimes (interior: KL wormhole, exterior: Schwarzschild or RN) are joined at a radius $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$2 greater than either the Schwarzschild/RN horizon or the KL throat radius. The shell at $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$3 supports surface stress-energy satisfying generalized Israel junction conditions. The dynamics and stability of the shell are governed by the master inequalities from GLV, which depend on:

• The second derivative of the "mass" function $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$4, where $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$5 is the surface energy density.
• The "external force" term $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$6, associated with the jump in the redshift functions' derivatives across the junction, reflecting the presence of nontrivial gravitational and electrostatic potentials.

A stable configuration requires both the "mass" and "external force" inequalities to be satisfied at the static equilibrium radius.

Schwarzschild-Kim-Lee Glued Wormholes with Scalar Charge

The stability analysis for the Schwarzschild exterior and scalar-charged KL interior reveals the following:

• The allowable region for stable configurations is demarcated by the surfaces $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$7 and $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$8, where the dimensionless parameters are $b(r) = b_0^{2\beta/(2\beta+1)} r^{1/(2\beta+1)}$9, $\beta = -1$0, $\beta = -1$1.
• Increasing the scalar charge $\beta = -1$2 reduces the stability region significantly; for $\beta = -1$3, only 38% of the original stability region (corresponding to $\beta = -1$4) remains.
• The wormhole's stability is sensitive to the scalar charge: large values of $\beta = -1$5 restrict the permitted radii and throat parameters for a stable shell.

Notably, in the limit $\beta = -1$6 (the massless Ellis-Bronnikov case), the results reproduce previously known stability bounds.

RN-Kim-Lee Glued Wormholes with Electric Charge

For glued configurations with an exterior RN black hole and interior electrically charged KL wormhole, the analysis similarly quantifies the allowed stability regions via dimensionless parameters $\beta = -1$7 and $\beta = -1$8. The findings are:

• When $\beta = -1$9, the stability region decreases monotonically as the common charge increases.
• For $$ds^2 = -dt^2 + \left(1 - \frac{b_0^2 - \alpha}{r^2}\right)^{-1} dr^2 + r^2(d\theta^2 + \sin^2\theta\, d\phi^2),$$0, increasing the interior wormhole's charge shrinks the stability region.
• Contrarily, for $$ds^2 = -dt^2 + \left(1 - \frac{b_0^2 - \alpha}{r^2}\right)^{-1} dr^2 + r^2(d\theta^2 + \sin^2\theta\, d\phi^2),$$1, increasing the exterior's charge expands the stability region, though the effect is quantitatively modest.
• In all cases, the region of stability is determined by the intersection where both mass and external force constraints are satisfied.

These results establish that the parameter space for stable configurations is highly sensitive to both the distribution and magnitude of charges in the glued geometry.

Implications and Theoretical Significance

The principal implication is that massless wormholes, which are otherwise unstable under physically reasonable perturbations, can be made linearly stable as the interior of a glued configuration via an appropriate choice of exterior geometry and shell radius. The massless KL wormhole's physical relevance is further underscored by its possible microlensing implications and phenomenological similarity to Ellis-Bronnikov wormholes. The thin-shell construction provides a framework where exotic matter distribution is localized on the shell, and the bulk interiors can have energy-momentum sources (e.g., phantom scalar or electric fields) tailored for stability.

From a theoretical standpoint, these results offer insight into the effect of backreaction and charge on thin-shell wormhole stability: while increased interior scalar or electric charge generally destabilizes the configuration, increased exterior (black hole) charge has a stabilizing influence when it exceeds the interior's. This dependence could inform future traversable wormhole models and might constrain or motivate searches for exotic compact lensing objects.

In quantum gravity and modified gravity contexts, the cut-and-paste construction and the detailed stability analysis outlined here may guide further exploration of wormhole solutions that achieve traversability without violating stability or energy conditions excessively.

Conclusion

The study demonstrates that massless KL wormholes, though individually unstable, become stable when realized as the interior sector of a glued thin-shell wormhole with a Schwarzschild or RN exterior. The stability regions are explicitly computed as functions of the source charges and shell parameters, revealing that only a restricted subset of parameter space is viable. These findings enhance the catalog of physically tenable wormhole solutions and suggest possible directions for further studies of thin-shell constructions, both in classical and quantum gravity. Future work may extend this analysis to rotating spacetimes, higher dimensions, or alternative gravitational theories.

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Reference: "Stability regions of glued wormholes with massless Kim-Lee backreacted spacetimes as interior" (2607.01687)