⚛️ general relativity

Decoding Horizonless Spacetime: Plasma-Induced Features in a Rotating Wormhole Shadow

This study investigates the shadow morphology of a rotating wormhole in a plasma environment using the Hamilton-Jacobi formalism, deriving constraints on its geometric and plasma parameters based on recent observational bounds on shadow radius deviations and identifying distinct optical features that differentiate it from Kerr black holes.

Original authors: Pabitra Gayen, Ratna Koley

Published 2026-02-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Pabitra Gayen, Ratna Koley

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, dark ocean. In this ocean, we usually look for "black holes," which are like cosmic whirlpools so deep that nothing, not even light, can escape once it gets too close. They leave a dark shadow on the water's surface.

But what if there are other objects in this ocean? Objects that look like whirlpools but don't have a bottom? These are wormholes. They are like tunnels connecting two different parts of the ocean. If you dive in one side, you pop out the other.

This paper is like a detective story. Two scientists, Pabitra and Ratna, are trying to figure out how to tell the difference between a Black Hole (the whirlpool with a bottom) and a Rotating Wormhole (the tunnel) just by looking at their shadows.

Here is the story of their investigation, broken down into simple parts:

1. The Setting: A Foggy, Spinning Tunnel

The scientists didn't just look at the wormhole in a vacuum. They imagined it surrounded by plasma.

The Analogy: Think of the wormhole as a lighthouse in a thick, swirling fog. The fog isn't just water vapor; it's a special kind of "space fog" made of charged particles (electrons).
The Effect: Just like how a straw looks bent when you put it in a glass of water, light bends when it travels through this plasma. The scientists had to calculate exactly how this "space fog" would distort the shadow of the wormhole.

2. The Tool: The "Magic Map"

To predict how light moves through this spinning, foggy tunnel, they used a mathematical tool called the Hamilton-Jacobi formalism.

The Analogy: Imagine trying to predict the path of a marble rolling on a bumpy, spinning table covered in syrup. It's incredibly hard to do by eye. But if you have a "Magic Map" (the math equation) that tells you exactly how the syrup and the spin affect the marble, you can draw the path perfectly.
The Breakthrough: They found a special way to draw this map that works even with the plasma fog, allowing them to predict exactly what the shadow would look like.

3. The Shadow: What Does It Look Like?

When light from a distant star hits the wormhole, some light gets sucked in, and some gets bent around it, creating a dark circle (the shadow) against the bright background.

The scientists found three main things:

The Shape Shift: If the wormhole spins fast, the shadow gets squashed and tilted, like a spinning top casting a weird shadow on the wall.
The Fog Effect: The amount of "fog" (plasma) changes the size of the shadow.
- In some types of fog, the shadow gets bigger.
- In other types of fog, the shadow gets smaller and can even disappear completely if the fog is too thick!
The "Deviation" Factor: The wormhole they studied has a "knob" called the deviation parameter ( $q$ $q$ ).
- If you turn this knob to zero, the wormhole looks exactly like a standard Black Hole (Kerr black hole).
- If you turn the knob, the shadow starts to look different, giving us a clue that it's a wormhole and not a black hole.

4. The Real-World Test: The Event Horizon Telescope

The scientists didn't just do this on paper; they checked their math against real photos taken by the Event Horizon Telescope (EHT), which took the first pictures of black holes (M87* and Sgr A*).

The Circular Test: They checked if the shadow was perfectly round. Real black holes are very round. The wormhole shadows were slightly off-center or oval-shaped. However, the EHT photos are so blurry that they couldn't use this "roundness" test to rule out the wormhole yet.
The Size Test: They measured the size of the shadow. The EHT gave a very specific size range for the black hole at the center of our galaxy (Sagittarius A*).
- The Result: By comparing their wormhole math to the real size, they found that for the wormhole to look like the real photo, it can't be too different from a black hole.
- The Constraint: They put "speed limits" on the wormhole. For example, the "deviation knob" ( $q$ ) can't be turned past a certain point (about 0.24), and the plasma fog can't be too dense. If it were, the shadow would look nothing like the photo we actually took.

5. The Big Conclusion

So, what did they learn?

Wormholes are tricky: They can mimic black holes very well, especially if they are spinning and surrounded by plasma.
Plasma is key: You can't understand the shadow without knowing how thick the "fog" is around the object. The type of fog changes the shadow's size and shape.
We are getting closer: While we can't say for sure yet if the object in the center of our galaxy is a wormhole or a black hole, this study gives us a checklist. If future telescopes get sharper pictures, we can look for these specific "wobbles" and "size changes" to finally say, "Aha! It's a wormhole!" or "Nope, it's definitely a black hole."

In a nutshell: The paper is a guidebook for astronomers on how to spot a cosmic tunnel disguised as a black hole, using the distortion of light caused by space-fog and the specific shape of its shadow.

1. Problem Statement

The Event Horizon Telescope (EHT) imaging of M87* and SgrA* has intensified the search for alternatives to Kerr black holes, specifically horizonless compact objects like rotating wormholes (WHs). While theoretical models exist, distinguishing a rotating wormhole from a Kerr black hole observationally remains challenging.

The Gap: Most existing studies analyze wormhole shadows in vacuum or simplified plasma environments. Real astrophysical environments contain cold, non-magnetized plasma that affects light propagation via refraction and frequency dependence.
The Objective: To investigate the shadow morphology of a recently proposed rotating wormhole geometry (a Kerr-like extension of the Damour–Solodukhin wormhole) in the presence of realistic plasma environments. The authors aim to identify unique observational signatures that can discriminate between wormholes and black holes and to constrain the wormhole's geometric and plasma parameters using current EHT observational bounds.

2. Methodology

The authors employ a semi-analytical approach combining general relativity with plasma electrodynamics:

Spacetime Geometry: They utilize a specific rotating wormhole metric derived by Azreg-Aïnou's method applied to a static Ricci-flat wormhole. The metric is characterized by three parameters:
- $M$ : ADM mass.
- $a$ : Spin parameter.
- $q$ : A dimensionless deviation parameter from the Kerr solution ( $q \to 0$ recovers Kerr).
- Note: This geometry lacks an ergosphere and possesses no curvature singularities.
Plasma Modeling: The environment is modeled as a cold, non-magnetized, pressureless, dispersive plasma. The light propagation is governed by a modified Hamiltonian derived from Maxwell's equations in curved spacetime:
$H(x, p) = \frac{1}{2} \{ g^{\mu\nu}p_\mu p_\nu + \omega_P(x)^2 \} = 0$
where $\omega_P$ is the plasma frequency proportional to the square root of the electron density.
Hamilton-Jacobi Formalism: To solve for photon trajectories, the authors apply the Hamilton-Jacobi equation. A critical requirement for separability (and the existence of a generalized Carter constant) is that the plasma frequency profile must satisfy a specific separability condition:
$\omega_P^2(r, \theta) = \frac{f_r(r) + f_\theta(\theta)}{r^2 + a^2 \cos^2 \theta}$
Three specific plasma density profiles are analyzed:
1. Homogeneous: Constant density.
2. Longitudinal: Density varies with the polar angle $\theta$ .
3. Radial: Density varies with the radial coordinate $r$ (modified to satisfy separability).
Shadow Calculation:
- The authors derive the equations of motion for light rays and identify unstable spherical photon orbits (photon regions) which define the shadow boundary.
- They calculate the celestial coordinates ( $\alpha, \beta$ ) for an asymptotic observer at inclination angle $\theta_o$ .
- They compute two key observational metrics:
  1. $\Delta C$ : Deviation from circularity (measuring asymmetry due to spin/frame-dragging).
  2. $\delta$ : Fractional deviation of the average shadow radius from that of a Schwarzschild black hole.

3. Key Contributions

Analytical Separability in Plasma: The paper successfully demonstrates that for specific plasma profiles, the Hamilton-Jacobi equation remains separable in this rotating wormhole geometry, allowing for the derivation of a generalized Carter constant. This enables analytical computation of shadow boundaries rather than relying solely on numerical ray tracing.
Plasma-Induced Morphology: The study reveals that plasma is not merely a background medium but actively reshapes the shadow. Depending on the profile, plasma can either enlarge or shrink the shadow size and alter its shape.
Parameter Constraints: The authors provide the first set of theoretical constraints on the deviation parameter ( $q$ ) and plasma density parameters ( $\rho, \rho_\theta, \rho_r$ ) by comparing their models against EHT observational data for SgrA* and M87*.

4. Key Results

A. Shadow Morphology and Plasma Effects

Homogeneous Plasma:
- As the plasma density parameter ( $\rho$ ) increases, the shadow size enlarges.
- The shadow shape coincides with the Kerr black hole shadow when $q=0$ .
- Increasing the deviation parameter $q$ causes the shadow to shrink and change shape.
Longitudinal and Radial Plasma:
- In contrast to the homogeneous case, increasing the plasma density parameters ( $\rho_\theta$ or $\rho_r$ ) causes the shadow size to monotonically shrink.
- Beyond a critical threshold density, the shadow vanishes entirely because photons are absorbed or cannot reach the asymptotic observer.
Spin and Inclination:
- Increasing the spin parameter $a$ causes a lateral shift of the shadow to the right in the observer's sky (due to frame-dragging).
- Higher inclination angles increase the deviation from circularity ( $\Delta C$ ).

B. Observational Constraints (EHT Bounds)

The authors used EHT bounds for SgrA* ( $\delta \in [-0.14, 0.01]$ ) and M87* ( $\Delta C \leq 0.10$ ) to constrain parameters:

Circularity ( $\Delta C$ ): The theoretical range of parameters satisfies the $\Delta C \leq 0.10$ bound for all allowed values of $q$ and plasma parameters. Thus, circularity alone cannot effectively constrain the wormhole parameters in this model.
Radius Deviation ( $\delta$ ): This provides stringent constraints.
- Longitudinal Plasma: Upper limits found are $q \approx 0.24$ , $a/M \approx 0.99$ , and $\rho_\theta \approx 3.2$ .
- Radial Plasma: Upper limits found are $q \approx 0.24$ , $a/M \approx 0.99$ , and $\rho_r \approx 4.0$ .
- Homogeneous Plasma: An upper bound of $\rho \approx 1$ was found, but no definitive limit could be placed on $q$ using current data.

C. Discriminants

The paper identifies that the intensity contrast between the interior and exterior of the photon ring, and the specific monotonic shrinking behavior of shadows in non-homogeneous plasma, could serve as discriminants to distinguish rotating wormholes from Kerr black holes.

5. Significance

Astrophysical Realism: By incorporating frequency-dependent plasma effects, the study moves beyond idealized vacuum models, offering a more realistic prediction for radio-band observations (where EHT operates).
Testing Gravity: The results provide a framework to test the "horizonless" hypothesis. If future observations show shadow sizes shrinking with specific plasma density profiles (as predicted for longitudinal/radial models) or specific deviations in $\delta$ , it could rule out standard Kerr black holes in favor of wormhole geometries.
Parameter Space Mapping: The derived bounds on the deviation parameter $q$ and plasma densities offer a concrete target for future high-resolution interferometry. It suggests that while wormholes are theoretically viable, their parameters must lie within narrow ranges to be consistent with current EHT data.
Future Directions: The authors highlight that incorporating magnetized plasma, full MHD accretion flows, and analyzing light sources on the "other side" of the wormhole throat are necessary next steps for a complete observational signature.