⚛️ general relativity

Observational Signatures of Static and Rotating Wormholes Embedded in Dark Matter

This paper demonstrates that the observational signatures of static and rotating wormholes, including shadow size, photon-ring sharpness, and accretion disk appearance, are distinctly shaped by their surrounding dark matter profiles, with solitonic wave dark matter supporting a genuine photon sphere and offering a unique probe of ultralight boson mass that the cuspy Navarro-Frenk-White halo lacks.

Original authors: Zinnat Hassan, Paras Balani, P. K. Sahoo

Published 2026-08-12

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CC BY 4.0

Original authors: Zinnat Hassan, Paras Balani, P. K. Sahoo

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

Imagine the universe as a giant, invisible ocean. For decades, scientists have known that most of this ocean isn't made of the water we can see (stars, planets, us), but of something invisible called "dark matter." It's the ghostly scaffolding that holds galaxies together, preventing them from flying apart. But here's the mystery: what is this ghost made of? Is it a swarm of tiny, invisible particles acting like a cold, dense fog? Or is it a giant, wavy quantum field, like a cosmic ocean wave that can form solid-looking blobs?

To solve this, scientists look at the most extreme places in the universe, like the centers of galaxies, where gravity is so strong it can bend light itself. They also look at wild theoretical ideas, like "wormholes." Think of a wormhole not as a sci-fi tunnel, but as a bridge connecting two distant points in space-time, like folding a piece of paper and poking a hole through it. If a wormhole existed, it would act like a cosmic lens, bending light in very specific ways. By studying how light behaves around these bridges, we might be able to tell if the dark matter surrounding them is a cold fog or a quantum wave.

This paper takes that idea and runs a massive simulation to see what happens. The authors, Zinnat Hassan, Paras Balani, and P.K. Sahoo, decided to build two different types of wormholes. They didn't just imagine them in empty space; they embedded them in two very different "dark matter neighborhoods." One neighborhood is the NFW halo, which is like a sharp, steep cone of dark matter that gets denser and denser as you get closer to the center (a "cusp"). The other is the Soliton halo, which is like a fluffy, soft ball of quantum waves that stays flat and spread out in the middle (a "core"). They used real data from a dwarf galaxy called NGC 2366 to make sure their numbers were realistic.

The team then asked: "If we shine a flashlight at these wormholes, what does the shadow look like?" They simulated the paths of light rays (photons) as they zoomed past these bridges, accounting for both static (still) wormholes and slowly spinning ones.

Here is what they found:

The "Cone" vs. The "Ball"
The two types of dark matter created very different results.

The NFW (Cone) Wormhole: Because the dark matter here is shaped like a steep cone, the gravity isn't quite strong enough to trap light in a perfect circle far away from the wormhole. Instead, the light just grazes the throat of the wormhole. The "shadow" (the dark spot where light gets swallowed) is almost exactly the same size as the wormhole's opening. It's a bit like trying to catch a ball in a shallow bowl; the ball just rolls right off the edge.
The Soliton (Ball) Wormhole: The fluffy, quantum-wave dark matter is much more focused. It creates a gravity well deep enough to trap light in a distinct, unstable circle outside the wormhole itself. This creates a "photon sphere"—a ring of light that orbits the wormhole before falling in or escaping. Because of this, the shadow is noticeably larger (about 18% to 26% bigger) than the wormhole's actual opening. It's like the ball of dark matter acts as a magnifying glass, pushing the shadow outward.

The Spin and the Twist
When the authors made the wormholes spin, things got even more interesting. Spinning objects drag space-time around with them (a bit like a spinning spoon dragging honey).

For the NFW wormhole, the spin made the shadow slightly lopsided, but the edge remained fuzzy because there was no distinct ring of light to sharpen it.
For the Soliton wormhole, the spin also made the shadow lopsided, but the distinct ring of light remained sharp. This "ring sharpness" is a key clue. It tells us that the dark matter isn't just a cold fog; it has a wave-like structure that can hold light in a tight orbit.

The Secret Code
The most exciting discovery is that the Soliton wormhole's shadow size depends on the "mass" of the dark matter particle. If the particle is very light (around $10^{-18}$ eV), the shadow becomes huge, and almost all light gets trapped. If the particle is heavier, the shadow shrinks. This means that by measuring the size of a wormhole's shadow, we could theoretically figure out the mass of the dark matter particle itself. The NFW model doesn't have this feature; its shadow size only tells you how big the wormhole is, not what the dark matter is made of.

What This Means
The paper suggests that if we ever find a wormhole (or a similar exotic object) in a galaxy, the way its shadow looks could be the "smoking gun" that proves dark matter is made of these ultra-light quantum waves rather than cold particles. The Soliton model produces a sharper, larger shadow with a distinct ring, while the NFW model produces a softer, smaller shadow that hugs the wormhole's throat.

However, the authors are careful to note that these are simulations based on current theories. We haven't actually seen a wormhole yet. But this work provides a clear "recipe" for what to look for. If future telescopes (like the Square Kilometre Array) spot a giant, dark, arc-minute-sized hole in a dwarf galaxy with a sharp, bright ring around it, it might not just be a wormhole—it could be the first direct proof that dark matter is a giant, cosmic quantum wave.

Technical Summary: Observational Signatures of Static and Rotating Wormholes Embedded in Dark Matter

Problem Statement
The paper addresses the observational distinguishability of traversable wormholes when embedded in realistic galactic dark matter environments. While wormholes are theoretically viable alternatives to black holes in General Relativity (GR), their observational signatures are often modeled using idealized metrics or vacuum solutions. This study investigates how two contrasting dark matter (DM) density profiles—the cuspy Navarro–Frenk–White (NFW) halo and the cored solitonic wave dark matter ( $\psi$ DM) profile—fundamentally alter the spacetime geometry and photon dynamics of static and slowly rotating wormholes. The work is motivated by the "cusp-core problem" in cosmology, where NFW profiles (predicted by $\Lambda$ CDM simulations) fail to match the flat cores observed in dwarf galaxies, whereas solitonic models (arising from ultralight bosonic fields) naturally produce such cores. The authors utilize parameters constrained by the rotation curve of the dwarf galaxy NGC 2366 to ensure astrophysical relevance.

Methodology
The authors employ the Morris–Thorne framework for static wormholes and the Teo metric for slowly rotating wormholes. The methodology proceeds as follows:

Metric Construction: The Einstein field equations are solved within the Morris–Thorne framework using the NFW and solitonic DM density profiles as source terms. This yields specific shape functions $b(r)$ and redshift functions $\Phi(r)$ for both static cases. For rotating cases, a Lense–Thirring frame-dragging term $\omega(r) \approx 2J/r^3$ is introduced.
Geodesic Tracing: Null geodesics are integrated numerically to trace photon trajectories. The study analyzes the existence and location of photon spheres (unstable circular photon orbits) by solving for the extremum of the effective potential.
Observables Calculation:
- Shadow Maps: Critical impact parameters ( $b_{ph}$ ) are computed to define the shadow boundary.
- Intensity Profiles: Specific intensity $I(\tilde{b})$ is calculated using path-length weighted transfer integrals, accounting for the Liouville invariant and redshift.
- Accretion Disk Imaging: Geometrically thin, optically thin accretion disks are simulated. The full relativistic Doppler effect (gravitational redshift and kinematic beaming) is incorporated via the redshift factor $g$ , with intensity scaling as $g^4$ .
Parameter Space: The analysis covers six throat radii ( $r_0 \in [0.2, 2.5]$ kpc) and, for rotating cases, three angular momentum values ( $J \in \{0, 0.3, 0.6\}$ kpc $^2$ ). The soliton model is further tested against variations in the ultralight boson mass ( $m_b$ ).

Key Contributions and Results

Photon Sphere Bifurcation: The most significant geometric finding is a qualitative divergence in photon dynamics between the two models.
- NFW Model: The NFW potential is too shallow to support a detached photon sphere. The condition for an unstable circular orbit ( $r\Phi'(r)=1$ ) is never met outside the throat. Consequently, the critical impact parameter is determined almost entirely by the throat radius ( $b_{ph} \approx 1.05 r_0$ ), and the shadow boundary coincides with the throat.
- Soliton Model: The solitonic core is sufficiently dense to create a potential deep enough to host a true, unstable photon sphere at a radius $r_{ph} > r_0$ . This results in a critical impact parameter $b_{ph} \approx 1.18 - 1.26 r_0$ , creating a distinct separation between the throat and the photon ring.
Static Observables:
- Shadow Size: The soliton shadow is approximately 15–20% larger than the NFW shadow for the same throat radius.
- Ring Sharpness: The NFW shadow boundary is diffuse, defined by throat-grazing deflection. The soliton shadow features a sharper, brighter photon ring sourced by the genuine unstable orbit.
- Boson Mass Sensitivity: A unique result for the soliton model is the dependence of the photon sphere on the boson mass $m_b$ (via $\rho_c \propto m_b^{-2}$ ). A transition occurs near $m_b \sim 10^{-18}$ eV: lighter bosons create dense cores that lead to total photon capture (no deflected rays), while heavier bosons allow for a deflecting regime with a detached photon sphere. This transition is absent in the NFW case.
Rotating Observables:
- Frame Dragging: Rotation introduces asymmetry in the shadow and accretion disk images. The critical impact parameter splits into co-rotating ( $b_-$ ) and counter-rotating ( $b_+$ ) branches.
- Centroid Offset: The shadow centroid shifts by $\Delta b_{ph}/2 \approx 2J/r_{ph}$ . While the NFW model allows a direct determination of angular momentum $J$ from the shadow size (since $r_{ph} \approx r_0$ ), the soliton model introduces a degeneracy where $r_{ph}$ depends on halo microphysics. However, the soliton model retains a sharper photon ring under rotation, serving as a discriminator.
- Disk Morphology: Both models exhibit Doppler-induced brightness asymmetry and secondary images. However, the soliton disk displays a more compact secondary image and a sharper transition at the dark region boundary due to the underlying photon sphere.

Significance and Claims
The paper claims that the microphysical nature of dark matter leaves a systematic, multi-faceted imprint on the optical signatures of wormholes. The primary significance lies in demonstrating that the presence or absence of a detached photon sphere is a direct probe of the dark matter profile's inner structure (cuspy vs. cored).

Specifically, the authors assert that:

Direct Probe of DM Microphysics: The soliton wormhole offers a unique observational handle on the mass of ultralight bosons ( $m_b$ ) through the lensing regime transition (total capture vs. deflection) and the specific size of the shadow, a capability missing in NFW-based models.
Observational Pathway: While the predicted angular sizes (arcminutes at Mpc distances) are too large for current Event Horizon Telescope (EHT) resolution (which targets microarcsecond horizon scales), the results propose a pathway for future wide-field radio continuum mapping (e.g., with the Square Kilometre Array) to detect extended low-surface-brightness absorption features in dwarf galaxies.
Differentiation: The combination of shadow size, photon-ring sharpness, and centroid displacement provides a robust method to distinguish between NFW and solitonic dark matter halos, even in the presence of rotation.

The work concludes that strong-field gravitational lensing of halo-scale compact objects offers a qualitatively new approach to probing the quantum nature of dark matter, bridging the gap between compact object astrophysics and dark sector microphysics.

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