⚛️ general relativity

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

This paper investigates the stability regions of traversable wormholes formed by gluing massless, backreacted Kim-Lee interior spacetimes (both scalar and electrically charged) to massive Schwarzschild and Reissner-Nordström exteriors via thin shells, demonstrating that despite the distinct physical nature of the interiors, the resulting stability conditions are remarkably similar.

Original authors: G. F. Akhtaryanova, R. Kh. Karimov, R. N. Izmailov, A. Bhattacharya

Published 2026-07-03

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: G. F. Akhtaryanova, R. Kh. Karimov, R. N. Izmailov, A. Bhattacharya

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: Fixing a Wobbly Bridge

Imagine a wormhole as a magical tunnel connecting two distant places in the universe. In physics, there is a specific type of wormhole called the Kim-Lee (KL) wormhole. Think of this wormhole as a "ghost bridge"—it has no weight (zero mass) and is incredibly useful for things like cosmic lensing (bending light), but it has a fatal flaw: it is unstable.

If you try to build this ghost bridge on its own, it's like trying to balance a house of cards in a hurricane. The slightest breeze (a tiny disturbance) causes it to collapse instantly.

The authors of this paper asked a simple question: Can we make this wobbly, weightless bridge stable by attaching it to something heavy and sturdy?

The Solution: The "Glued" Sandwich

To solve the instability problem, the researchers proposed a "cut-and-paste" surgery. They took the unstable, weightless Kim-Lee wormhole (the interior) and glued it to a massive, heavy black hole (the exterior) using a thin, magical shell in the middle.

Think of it like this:

The Interior: A fragile, weightless soap bubble (the Kim-Lee wormhole).
The Exterior: A heavy, solid steel ball (a Schwarzschild or Reissner-Nordström black hole).
The Glue: A thin, invisible shell that holds them together.

The goal was to see if the heavy steel ball could stabilize the soap bubble. The paper finds that yes, it can. The heavy exterior acts like a stabilizing anchor, allowing the weightless interior to exist without collapsing, provided the "glue" (the thin shell) is placed at just the right distance.

The Two Experiments

The researchers tested this "gluing" idea in two different scenarios, like testing two different types of glue:

The Scalar Charge Experiment: They glued the weightless wormhole to a standard black hole. However, the wormhole had a "scalar charge" (a type of invisible energy field). They found that as you increased this charge, the "safe zone" where the bridge stays stable got smaller. It's like adding more weight to the soap bubble; it becomes harder to keep it stable, even with the steel ball holding it.
The Electric Charge Experiment: They glued the wormhole to a charged black hole (Reissner-Nordström). Here, both the black hole and the wormhole had electric charges. They tested three situations:
- Equal Charges: If both sides have the same charge, increasing the charge makes the stable area shrink.
- Weak Exterior, Strong Interior: If the outside black hole has a weak charge and the inside wormhole has a strong charge, increasing the inside charge shrinks the stable area.
- Strong Exterior, Weak Interior: If the outside black hole has a strong charge and the inside wormhole has a weak charge, increasing the outside charge actually expands the stable area. It's as if a stronger magnetic pull from the outside helps hold the fragile bubble in place better.

The "External Force" and "Mass" Rules

To prove the bridge wouldn't collapse, the authors used a special set of mathematical rules (developed by Garcia, Lobo, and Visser) that act like a safety inspector. They checked two main things:

The "Mass" Rule: Does the weight of the shell keep the structure together?
The "External Force" Rule: Are there invisible pushes or pulls (caused by the way the space curves) that might tear the shell apart?

The paper maps out a "stability map" (shown as shaded yellow areas in their figures). If your wormhole parameters fall inside this yellow zone, the bridge is safe. If you step outside the zone, the bridge collapses.

The Main Takeaway

The most important discovery is that a massless wormhole doesn't have to be unstable.

While a standalone Kim-Lee wormhole is like a house of cards that falls over immediately, a Kim-Lee wormhole that is "glued" to a massive black hole can be perfectly stable. It's like taking that house of cards and gluing it to a concrete foundation; the cards themselves are still light and fragile, but the whole structure stands firm.

The paper concludes that these "glued" wormholes are a promising new way to think about stable, massless tunnels in space, but they only work within very specific, limited conditions (the "yellow zones" on their maps). If the charges or distances are off, the stability vanishes.

Technical Summary: Stability Regions of Glued Wormholes with Massless Kim-Lee Backreacted Spacetimes as Interior

Problem Statement
Asymptotic zero Arnowitt-Deser-Misner (ADM) mass wormholes, such as the traversable Ellis-Bronnikov wormhole, are of significant interest for astrophysical applications like galactic microlensing. However, when considered as isolated entities, these massless wormholes are generally unstable under small perturbations. While the exterior spacetime of a glued configuration may possess non-zero ADM mass, the interior partner can remain massless. The central problem addressed in this paper is whether a massless Kim-Lee (KL) wormhole, which is typically unstable, can achieve stability when constructed as the interior partner of a traversable "glued" wormhole. This is achieved by joining the massless interior to observationally relevant massive exterior spacetimes (Schwarzschild and Reissner-Nordström) across a spherically symmetric thin shell.

Methodology
The authors employ the formalism developed by Garcia, Lobo, and Visser (GLV) to analyze the linear stability of the thin-shell dynamics. The study involves two specific models constructed via a "cut and paste" procedure:

Model 1: A scalar-charged, massless KL wormhole (interior) glued to a Schwarzschild vacuum (exterior).
Model 2: An electrically charged, massless KL wormhole (interior) glued to a Reissner-Nordström (RN) black hole (exterior).

In both cases, the interior regions (containing the wormhole throats) and the exterior regions (containing event horizons) are surgically excised, and the remaining manifolds are joined at a static radius $a_0$ . The stability analysis relies on two novel constraints derived by GLV:

The "mass" constraint, derived from the second derivative of the thin-shell mass $m_s(a)$ with respect to the radius.
The "external force" constraint, arising from the discontinuity in the conservation law of surface stresses due to non-zero redshift functions ( $\Phi'_{\pm} \neq 0$ ).

The authors derive the equations of motion for the shell, calculate the surface energy density ( $\sigma$ ) and surface pressure ( $\mathcal{P}$ ), and determine the stability regions in the dimensionless parameter space defined by $x = M/a_0$ , $y = b_0/M$ , and charge ratios ( $k = \alpha/b_0^2$ for scalar charge, $q = Q/b_0$ for electric charge).

Key Contributions and Results

Stabilization of Massless Interiors: The paper demonstrates that while massless KL wormholes are individually unstable, they can be stabilized as interior partners in a glued configuration. The stability is not inherent to the interior metric alone but is a property of the coupled system defined by the thin-shell dynamics.
Scalar-Charged Case (Schwarzschild-KL):
- The stability region is determined by the intersection of the "mass" and "external force" constraints in the $(x, y)$ plane.
- The analysis reveals that increasing the scalar charge parameter $\alpha$ (represented by $k$ ) significantly reduces the stability region. For instance, increasing $k$ from 0 to 0.9 reduces the stability region to approximately 38% of its maximum value (the case where $k=0$ , corresponding to the Ellis-Bronnikov wormhole).
- Stability is only achieved for specific ranges of parameters, specifically $x > 0.45$ and $y > 3.5$ in the high-charge limit.
Electrically Charged Case (RN-KL):
- The study investigates three scenarios based on the ratio of the exterior RN charge ( $q_{RN}$ $q_{R N}$ ) to the interior KL charge ( $q_{KL}$ $q_{K L}$ ):
  1. $q_{RN} = q_{KL}$ : Increasing the charge leads to a decrease in the stability region (e.g., a 47% reduction when charges reach 0.9).
  2. $q_{RN} < q_{KL}$ : When the exterior charge is fixed and the interior charge increases, the stability region decreases (e.g., a 53% reduction when $q_{KL}$ increases to 0.9).
  3. $q_{RN} > q_{KL}$ : Conversely, when the exterior charge increases while the interior charge is fixed, the stability region increases (e.g., a 5.5% increase when $q_{RN}$ rises to 0.9).
- This indicates that the relative magnitude of the charges plays a critical role in determining the stability boundaries.

Significance and Claims
The paper claims that the primary significance of this work lies in identifying a mechanism to stabilize massless wormholes that are otherwise unstable. By acting as an interior partner in a glued configuration, the massless KL wormhole preserves its zero ADM mass property while acquiring stability through the dynamics of the thin shell.

The authors modestly conclude that KL wormholes represent intriguing examples of objects born from cut-and-paste surgery that remain massless even after backreaction effects are considered. The study does not claim universal stability; rather, it establishes that stability is achievable only within limited, specific parametric regions defined by the mass and charge constraints. The work provides a detailed analysis of these stability features, offering a theoretical framework for understanding how massless wormholes might exist as stable components of larger astrophysical structures.

The Big Idea: Fixing a Wobbly Bridge

The Solution: The "Glued" Sandwich

The Two Experiments

The "External Force" and "Mass" Rules

The Main Takeaway

More like this