Traversable wormholes inside anisotropic magnetized neutron stars: physical properties and potential observational imprints

This paper investigates the physical properties of traversable wormhole-plus-neutron-star systems supported by scalar fields, demonstrating that the inclusion of fluid anisotropy and magnetic fields can lead to extremely massive configurations and distinctive gravitational-wave echo signals.

The Gist

Imagine you are looking at a map of the universe. Usually, we see stars and planets as solid objects, like islands in an ocean. But physicists have long wondered about "shortcuts"—tunnels through space called wormholes that could connect two distant points.

This paper explores a very specific, wild idea: What if a wormhole wasn't just floating in empty space, but was actually tucked inside a massive, spinning, magnetic star (a neutron star)?

Here is the breakdown of their discovery using everyday analogies.

1. The "Swiss Cheese" Star (The WH+NS System)

Think of a normal neutron star as a solid, incredibly dense bowling ball made of pure matter. Now, imagine that inside this bowling ball, there is a tiny, hollow tunnel—a wormhole.

The researchers aren't just looking at a simple hole; they are looking at a "hybrid" object. It’s like a Swiss cheese ball, where the "cheese" is the ultra-dense star matter and the "holes" are the wormholes. This creates a "Wormhole-plus-Neutron-Star" (WH+NS) system.

2. The "Pressure Cooker" Problem (Anisotropy and Magnetism)

In a normal star, the pressure pushes out equally in all directions, like air inside a balloon. But the authors added two "chaos factors":

• Anisotropy (The Uneven Push): Imagine a crowd of people in a room. If everyone pushes outward equally, it’s "isotropic." But if people are pushing harder toward the walls than they are toward each other, that’s "anisotropic." This uneven pressure changes how the star holds itself together.
• Magnetic Fields (The Invisible Cage): They added massive magnetic fields—think of these as invisible, super-strong rubber bands wrapping around the star. These fields add extra "magnetic pressure" that can change the star's weight and size.

3. The "Ghost" in the Machine (Eliminating Instabilities)

In the math used to build these wormholes, a problem often arises called "ghosts." In physics, a "ghost" isn't a spooky spirit; it’s a mathematical error that suggests the system is unstable and would instantly explode or collapse.

The researchers used a clever mathematical trick (called "Lagrange multipliers") to "exorcise" these ghosts. They essentially built a mathematical cage that keeps the wormhole stable so it doesn't vanish the moment it's created.

4. How would we spot one? (The Observational Imprints)

Since we can't fly a spaceship to a wormhole to check, we have to look for "fingerprints" left behind. The paper suggests two main ways:

• The "Extreme Redshift" (The Slow-Motion Effect): Gravity is so strong near these objects that it stretches light. If you looked at a light bulb inside this hybrid star, the light would look incredibly "reddened" and stretched out. The authors found that these objects could have a "redshift" much higher than any normal star, acting like a giant cosmic magnifying glass that slows down time and light.
• The "Gravitational Echo" (The Cosmic Hallway): Imagine you are in a long, narrow hallway and you clap your hands. You hear an echo. If a gravitational wave (a ripple in space) hits this hybrid star, it can get trapped in the "tunnel" of the wormhole and bounce back and forth. This would create a specific "echo" signal that our gravitational-wave detectors (like LIGO) could potentially hear. It would sound like a "thump... thump... thump..." instead of the usual single "crash" of a black hole collision.

The Big Takeaway

The researchers found that adding magnetism and uneven pressure makes these objects massive monsters. Some of these hybrid stars could be much heavier than the heaviest neutron stars we’ve ever seen.

In short: They have provided a mathematical blueprint for a "cosmic shortcut" hidden inside a star, and they’ve told astronomers exactly what kind of "echoes" and "colors" to look for in the sky to prove they exist.

Technical Summary

Technical Summary: Traversable Wormholes Inside Anisotropic Magnetized Neutron Stars

1. Problem Statement

The paper addresses the theoretical construction and physical viability of hybrid compact objects consisting of a traversable wormhole embedded within a neutron star (WH+NS). While previous studies have explored wormhole-plus-black-hole or wormhole-plus-compact-star systems, they often suffer from two major theoretical and physical limitations:

• Instabilities (Ghosts): Many models rely on scalar fields that behave as "ghosts" (fields with negative kinetic energy), leading to physical instabilities.
• Oversimplification: Existing models frequently neglect two critical astrophysical realities of neutron stars: pressure anisotropy (where radial and tangential pressures differ) and the presence of strong magnetic fields (magnetar-strength fields).

The authors aim to formulate a ghost-free WH+NS model that incorporates both fluid anisotropy and chaotic magnetic fields to determine if these factors alter the system's mass, radius, and potential observational signatures.

2. Methodology

The authors employ a General Relativity (GR) framework coupled with two auxiliary scalar fields ($\phi, \chi$). The methodology is structured as follows:

• Ghost Elimination: To prevent ghost instabilities, the authors introduce Lagrange multipliers ($\Lambda_\phi, \Lambda_\chi$) into the action. This imposes constraints that ensure the scalar fields act as non-propagating auxiliary variables that generate effective exotic matter (required for the wormhole throat) without introducing unstable degrees of freedom.
• Matter Modeling:
  • Anisotropy: They utilize the Cosenza-Herrera-Esculpi-Witten (CHEW) model, where anisotropy is parameterized by a constant $h$. The system is isotropic when $h=1$.
  • Magnetic Fields: They adopt a chaotic magnetic field ansatz, where the magnetic field is coupled to the energy density. This approach ensures the magnetic pressure is statistically isotropic, maintaining the spherical symmetry of the metric.
• Mathematical Framework: The authors solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations for the interior of the star. They use a polytropic Equation of State (EOS) and a Tolman-VII-like energy density profile.
• Comparative Approaches: To analyze the Mass-Radius (MR) relation, they use two distinct construction schemes:
  • Approach 1: Fixes the stellar surface radius ($R_s$) to match an ordinary neutron star at the same central density.
  • Approach 2: Fixes the total ADM mass ($M$) to match an ordinary neutron star.

3. Key Contributions

• Unified Formalism: A robust, ghost-free mathematical model for WH+NS systems that accounts for both anisotropy and magnetic fields.
• Analytical Solutions: Derivation of the metric functions and the relationship between the wormhole throat radius ($r_0$) and the ADM mass ($M = r_0/2$).
• Observational Imprint Analysis: The study provides quantitative predictions for surface redshift ($z$) and gravitational-wave echo time ($\tau$), offering a roadmap for detecting these objects via future gravitational-wave observatories (LIGO/Virgo).

4. Results

• Traversability: The Null Energy Condition (NEC) is consistently violated at the wormhole throat, ensuring the geometry remains traversable regardless of anisotropy or magnetic field strength.
• Mass and Radius Extremes:
  • Approach 1: The inclusion of magnetic fields and anisotropy allows for extremely massive configurations. For high anisotropy ($h=2$) and strong magnetic fields ($B_s = 10^{16}$ G), the ADM mass can exceed $14 \, M_\odot$, significantly higher than standard neutron stars.
  • Approach 2: This approach leads to "ultracompact" objects with extremely small radii (sub-kilometer scale) and low masses.
• Surface Redshift: The models predict surface redshifts $z > 1.5$, which is much higher than the typical $z \simeq 0.1–0.5$ observed in standard neutron stars.
• Gravitational-Wave Echoes:
  • The echo time $\tau$ is found to be in the millisecond ($10^{-1}$ ms) or microsecond ($10^{-2}$ $\mu$s) range.
  • Magnetic Effect: Strong magnetic fields increase the echo time by increasing the stellar radius. However, at extremely high field strengths ($\sim 10^{16}$ G), the echo time begins to decrease, a phenomenon explained by a toy model showing a sharp drop in the propagation path.

5. Significance

This research demonstrates that wormholes could theoretically exist within the extreme environments of magnetized, anisotropic neutron stars. The study is significant because it moves beyond idealized mathematical constructs to provide physically motivated models that produce distinctive, detectable signatures. Specifically, the combination of high mass (exceeding the secondary component of GW190814), high surface redshift, and specific gravitational-wave echo timings provides a clear "fingerprint" that could allow astronomers to distinguish a wormhole-star hybrid from a standard black hole or neutron star.