⚛️ general relativity

Optical constraints on rotating logarithmic- and exponential-entropy wormholes from strong-field lensing

This paper demonstrates that while the shadow diameter of rotating logarithmic- and exponential-entropy wormholes is degenerate with that of Kerr black holes, a multi-parameter observational fingerprint combining rotational asymmetry, strong-deflection lensing coefficients, Lyapunov exponents, and orbital frequencies can effectively distinguish these horizonless objects from black holes.

Original authors: A. Errehymy G. Yergaliyeva, S. K. Maurya, B. Turimov, I. Ibragimov, J. Rayimbaev

Published 2026-10-20

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CC BY 4.0

Original authors: A. Errehymy G. Yergaliyeva, S. K. Maurya, B. Turimov, I. Ibragimov, J. Rayimbaev

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

Deep in the fabric of space and time, gravity acts as a sculptor, bending light and warping the paths of everything that moves. For decades, the most famous result of this cosmic sculpting has been the black hole: a region so dense that nothing, not even light, can escape its pull once it crosses a point of no return called the event horizon. But for a long time, physicists have wondered if nature might have built something else entirely. Could there be a compact object that looks almost exactly like a black hole from the outside, yet lacks that fatal trap? These hypothetical structures are called wormholes. They are tunnels connecting two distant regions of space, or perhaps two different universes, held open by a throat that light can pass through. The problem is that, until now, we have had no way to tell the difference between a black hole and a wormhole just by looking at them. Both cast a dark shadow against the bright background of glowing gas, and for a long time, the size of that shadow seemed to be the only thing we could measure.

A new study published in the Journal of Cosmology and Astroparticle Physics takes a fresh look at this puzzle. The researchers, a team of physicists from universities in South Africa, Kazakhstan, Oman, Uzbekistan, and China, set out to design a specific type of rotating wormhole and then calculate exactly how it would appear to a telescope. They focused on a scenario where the wormhole is supported by "exotic" matter—a form of energy that behaves differently from the stars and gas we see every day. In standard physics, gravity pulls things together, but the matter needed to keep a wormhole open must push outward to prevent the tunnel from collapsing. The team used mathematical models based on how entropy, or disorder, behaves at the quantum level to create two distinct versions of these tunnels: one shaped by a logarithmic pattern and another by an exponential pattern. They then spun these wormholes up, adding rotation to see how the twisting of space would change the light passing near them.

The most surprising discovery is that if you only look at the size of the dark shadow, you cannot tell these wormholes apart from a spinning black hole. The researchers found that by adjusting a few internal parameters, the shadow of their wormhole models could be made to match the shadow of a standard black hole to within about five to eleven percent. This means that a telescope like the Event Horizon Telescope, which has already photographed the shadow of a black hole, might see a wormhole and simply think it is a black hole. The shadow diameter alone is a poor detective; it is too easily fooled.

However, the team realized that the shadow is just the beginning of the story. To truly identify what they are looking at, astronomers need to examine the finer details of how light behaves right at the edge of the darkness. The researchers calculated several other features that act as a unique fingerprint for these objects. First, they looked at how the shadow is distorted by the spin. Because the wormhole is rotating, it drags space around with it, making the shadow slightly squashed on one side and stretched on the other. They found that the wormholes in their models showed a slightly different amount of this squashing compared to a black hole. Second, they analyzed how light bends when it passes very close to the object. Light that grazes the edge doesn't just go straight; it loops around, creating a series of faint, ghostly images. The brightness and spacing of these images depend on the geometry of the object. The study showed that the wormholes produce these secondary images with a different brightness pattern than black holes do.

Perhaps the most telling difference involves the stability of the light itself. Around a black hole, light can orbit in a precarious circle, but it is unstable; a tiny nudge sends it either falling in or flying away. The researchers calculated how quickly this instability grows, a measure known as the Lyapunov exponent. They found that for their wormholes, this instability grows more slowly than it does for a black hole. In practical terms, this means the ring of light surrounding a wormhole would be slightly sharper and more stable than the ring around a black hole. When the object vibrates or rings down after a disturbance, it does so at a slightly different frequency and for a slightly longer time.

By combining all these measurements—the shape of the shadow, the brightness of the ghostly images, the rate of instability, and the frequency of the vibrations—the researchers created a five-part signature. When they compared this signature to that of a standard black hole, they found a clear difference. While a single measurement might be ambiguous, the combination of all five factors creates a signal strong enough to distinguish a wormhole from a black hole with high confidence. The study suggests that if we can measure these subtle effects with enough precision, we could finally prove whether the dark shadows we see in the sky are truly black holes or something far more exotic. The work does not prove that wormholes exist, but it provides a concrete roadmap for how we might find them if they are out there, turning a theoretical curiosity into a testable prediction for the next generation of astronomical observations.

Technical Summary: Optical Constraints on Rotating Logarithmic- and Exponential-Entropy Wormholes

Problem Statement
The paper addresses the longstanding degeneracy in distinguishing horizonless compact objects (specifically traversable wormholes) from black holes using observational data. While the shadow diameter of a compact object is a primary observable, the authors note that this single metric is insufficient; a wide class of geometries, including various black hole models and wormholes, can produce shadow diameters that differ by less than 10–11% from the Kerr black hole solution. Consequently, the shadow diameter alone cannot uniquely identify the nature of the central object. The paper seeks to resolve this degeneracy by constructing a multi-parameter "fingerprint" derived from strong-field lensing, photon-orbit stability, and ringdown dynamics.

Methodology
The authors construct a family of slowly rotating, traversable wormhole models within the Morris–Thorne framework, incorporating entropy-inspired matter sources. The methodology proceeds as follows:

Geometry and Matter Source:
- The spacetime is modeled using the stationary, axisymmetric Teo metric.
- The matter supporting the wormhole throat is derived from entropy–geometry correspondence relations, introducing two distinct sectors based on corrections to the Bekenstein–Hawking entropy:
  - Logarithmic-inspired sector: Controlled by parameter $\alpha$ , yielding a rational density profile. For $\alpha < 0$ , the density is negative, satisfying the requirements for exotic matter.
  - Exponential-inspired sector: Controlled by parameter $\beta$ , yielding a non-perturbative, exponentially localized negative density profile.
- A new lapse function $G(r)$ is introduced, parameterized by a redshift scale $r_c$ and a dimensionless softening parameter $\sigma$ . This function interpolates between an exponential redshift profile ( $\sigma=0$ ) and a rational form ( $\sigma \to \infty$ ). Crucially, it remains finite and positive at the throat, ensuring no event horizon forms, and possesses an analytical logarithmic derivative that facilitates the calculation of optical observables.
Optical and Dynamical Analysis:
- Null Geodesics: The authors derive equatorial null geodesics to determine the photon-sphere radius ( $r_{ph}$ ), critical impact parameters ( $b_{\pm}$ ), and the resulting shadow radius ( $R_{sh}$ ) and rotational asymmetry ( $A_{rot}$ ).
- Strong-Deflection Lensing: Using the Bozza formalism, the authors calculate the strong-deflection coefficients $a$ and $b$ . These coefficients govern the position and brightness of relativistic images.
- Stability and Ringdown: The Lyapunov exponent ( $L$ ) is computed to characterize the instability of circular photon orbits. This is linked to the eikonal quasinormal mode (QNM) frequencies, where the real part corresponds to the orbital frequency ( $O_{ph}$ ) and the imaginary part to the damping rate ( $L$ ).
Comparative Framework:
- The wormhole models are compared against the Kerr black hole and four regular black hole benchmarks: Kazakov–Solodukhin, Nicolini–Smailagic–Spallucci, Modesto–Nicolini, and regularized Reissner–Nordström–de Sitter.
- A multi-parameter vector $\mathcal{F} = (A_{rot}, a, b, L, O_{ph})$ is defined to serve as a discriminative fingerprint.

Key Contributions and Results

Shadow Diameter Degeneracy: The study confirms that the shadow diameter ( $R_{sh}$ ) is highly tunable. By adjusting the entropy parameters ( $\alpha, \beta$ ) and the softening parameter ( $\sigma$ ), the wormhole shadow can be made to match the Kerr shadow within 5% to 11% ( $|R_{sh}^{WH}/R_{sh}^{Kerr} - 1| \lesssim 0.11$ ). This reinforces the conclusion that shadow size alone is a poor discriminator.
Distinctive Multi-Parameter Fingerprint: While the shadow size is degenerate, the combined set of observables breaks this degeneracy. The authors find systematic deviations for the wormhole models compared to Kerr and regular black holes:
- Rotational Asymmetry ( $A_{rot}$ ): Wormholes exhibit slightly higher asymmetry ( $\sim 0.044-0.045$ ) compared to Kerr ( $\sim 0.039$ ) at the same spin.
- Lensing Coefficients: The strong-deflection coefficient $a$ is lower for wormholes ($0.91-0.96$) than for Kerr ($1.00$). The coefficient $b$ is significantly less negative for wormholes ($-0.25$ to $-0.29$) compared to Kerr ($-0.40$), implying brighter relativistic images.
- Lyapunov Exponent ( $L$ ): The wormhole photon rings are more stable, with $L$ values ($0.21-0.23$) systematically lower than Kerr ($0.26$). This results in a higher quality factor ( $Q_{ring} = O_{ph}/L$ ) for the wormhole rings.
- Quasinormal Modes: The eikonal QNM frequencies show a lower real part (orbital frequency) and a lower imaginary part (damping rate) for wormholes compared to black holes.
Discrimination Power: The authors quantify the distinguishability using a signal-to-noise ratio (SNR) based on the fractional deviations of the five-component fingerprint. Assuming 10% measurement uncertainties, the combined signal yields:
- $SNR \approx 3.8$ to $3.9$ for distinguishing the wormhole from the Kerr black hole.
- $SNR \approx 3.7$ for distinguishing the wormhole from the Kazakov–Solodukhin benchmark.
- The coefficient $b$ (lensing brightness) and the Lyapunov exponent $L$ are identified as the most dominant contributors to this discrimination.

Significance and Claims
The paper claims that while rotating entropy-inspired wormholes can mimic black holes in terms of shadow size, they possess a distinct "optical fingerprint" when multiple strong-field observables are considered simultaneously. The introduction of the new lapse function allows for the decoupling of the shadow radius from the stability of the photon ring (Lyapunov exponent), providing a powerful diagnostic tool.

The authors assert that the combination of rotational asymmetry, strong-deflection lensing coefficients, Lyapunov exponent, and orbital frequency is sufficient to break the shadow-diameter degeneracy at the 10% measurement level. The results suggest that future high-precision observations of relativistic image brightness, photon ring stability, and ringdown frequencies could potentially distinguish between horizonless wormholes and regular black holes, even when their shadows appear nearly identical. The work remains modest in its scope, focusing on the theoretical derivation of these signatures within the slow-rotation regime and noting that rapid rotation and full quasinormal spectra are subjects for future investigation.

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