⚛️ general relativity

Testing Conformal Weyl Gravity with Plasma Modified Black Hole Shadows and EHT Constraints

This paper investigates the shadows of charged rotating de Sitter black holes in conformal Weyl gravity immersed in plasma, demonstrating that while plasma effects reduce shadow sizes similarly to general relativity, the distinct response to electric charge in conformal gravity offers a potential observational method to distinguish the theory from environmental propagation effects using EHT data.

Original authors: Zhichen Guan, Connor McMillin, Owen Gartlan, William Horner, Leo Rodriguez, Shanshan Rodriguez

Published 2026-10-28

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Zhichen Guan, Connor McMillin, Owen Gartlan, William Horner, Leo Rodriguez, Shanshan Rodriguez

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

Black holes are often imagined as perfect, silent spheres of darkness, but in reality, the space around them is rarely empty. Light traveling from a distant star to our telescopes does not move through a perfect vacuum; it often passes through a thin, hot soup of charged particles known as plasma. This material, which surrounds many black holes, acts like a lens, bending and slowing down light in ways that depend on the light's color and the density of the gas. For astronomers trying to understand the nature of gravity itself, this creates a significant challenge. When we look at the "shadow" of a black hole—the dark silhouette cast against the glowing gas behind it—we see a shape that is a mixture of two things: the warping of space caused by the black hole's gravity, and the refraction caused by the surrounding plasma. If we cannot separate these two effects, we might mistake a change in the gas for a change in the laws of physics.

This is the central puzzle tackled by a team of researchers studying a specific, theoretical version of a black hole. They focused on a model called Conformal Weyl Gravity, a theory that modifies Einstein's general relativity by adding extra mathematical terms to describe how gravity behaves at very high energies. In this theory, a spinning, charged black hole behaves differently than it does in standard Einstein gravity. The researchers wanted to know if the unique "fingerprint" of this new theory could still be seen when the black hole was immersed in plasma, or if the gas would simply hide the differences. By simulating how light travels through this environment, they found a way to tell the two theories apart, even when the plasma is present.

The study began by constructing a detailed map of how light rays move around a spinning, electrically charged black hole in this modified gravity theory. In standard Einstein gravity, the electric charge of a black hole affects its gravity in a specific, well-understood way. However, in the Conformal Weyl model, the charge contributes to the gravitational pull in a different manner, growing stronger as you move further away from the center. The researchers calculated the paths of light rays, known as geodesics, taking into account both this unusual gravity and the presence of a cold, non-magnetized plasma. They used a mathematical approach that allowed them to separate the motion of light into distinct parts, making it possible to track exactly how the plasma density and the black hole's charge influenced the light's journey.

One of the most striking findings was how the two theories responded to changes in the black hole's charge. In standard Einstein gravity, adding more electric charge to a spinning black hole makes its shadow appear slightly smaller. In the Conformal Weyl model, the opposite happens: increasing the charge makes the shadow significantly larger. This difference is crucial because it provides a clear way to distinguish between the two theories. If astronomers could measure the shadow of a black hole with enough precision, they could look for this specific trend. If the shadow grows as the charge increases, it would support the modified gravity theory; if it shrinks, it would support Einstein's original theory.

The researchers also examined how the plasma itself altered these shadows. They found that increasing the density of the plasma generally made the shadow appear smaller in both theories. This is because the plasma acts like a refractive medium, bending the light in a way that reduces the apparent size of the dark region. This effect creates a potential confusion: a dense cloud of plasma could make a black hole look smaller, mimicking the effect of charge in standard Einstein gravity. However, the team discovered that the two effects do not cancel each other out in a simple way. While the plasma shrinks the shadow in both cases, the way the shadow responds to charge remains distinct. In the modified theory, the charge still tries to expand the shadow, fighting against the plasma's shrinking effect, whereas in standard gravity, both the charge and the plasma work together to shrink it.

To see if these theoretical differences could be observed in the real universe, the team compared their results with actual images taken by the Event Horizon Telescope, which has captured the shadows of two famous black holes: Sagittarius A* at the center of our galaxy and M87* in a distant galaxy. They calculated what the size of the shadow would be for different combinations of charge and plasma density. Their analysis showed that for the black hole at the center of our galaxy, the presence of plasma is essential to explain the observed size. If the plasma were ignored, the allowed range of charge would be very different. Specifically, for the modified gravity theory to match the observed size of Sagittarius A*, the amount of plasma surrounding it must be relatively high. In contrast, for standard Einstein gravity, the plasma and charge constraints work in the same direction, allowing for a different set of possibilities.

The study concludes that while plasma can obscure some details of a black hole's gravity, it does not erase the fundamental differences between Einstein's theory and Conformal Weyl Gravity. The key lies in the opposite way the two theories react to electric charge. By carefully measuring the size of a black hole's shadow and accounting for the density of the surrounding plasma, astronomers may be able to test whether gravity behaves exactly as Einstein predicted or if it follows the more complex rules of Conformal Weyl Gravity. The researchers emphasize that this is not a definitive proof of one theory over the other, but rather a clear path forward. They have shown that the unique signature of the modified theory survives the interference of the plasma, offering a concrete target for future observations with more sensitive telescopes.

In the end, the work serves as a reminder that understanding the universe requires looking at the whole picture. We cannot simply look at the black hole and ignore the gas around it, nor can we assume that the gas is just a minor nuisance. The interplay between the extreme gravity of a black hole and the subtle physics of the plasma it inhabits creates a complex signal. By untangling these effects, scientists can begin to ask deeper questions about the nature of space, time, and the fundamental forces that shape our cosmos. The shadow of a black hole is not just a dark spot; it is a canvas where the laws of physics are painted in the light of distant stars, and with the right tools, we are learning how to read the brushstrokes.

Technical Summary: Testing Conformal Weyl Gravity with Plasma Modified Black Hole Shadows and EHT Constraints

Problem Statement
Black hole shadows and strong-field gravitational lensing serve as critical probes for testing General Relativity (GR) against modified gravity theories. However, observational data from the Event Horizon Telescope (EHT) for sources like Sgr A* and M87* are complicated by astrophysical environments, specifically the presence of plasma surrounding compact objects. Plasma introduces refraction and dispersion, making shadow boundaries and deflection angles frequency-dependent. A significant challenge in interpreting these observations is distinguishing between geometric deviations caused by the underlying gravitational theory (e.g., Conformal Weyl Gravity vs. GR) and those caused by environmental propagation effects (plasma). Previous studies often treated these factors separately or focused on vacuum solutions. This work addresses the need to jointly constrain the charge and plasma parameters within a fourth-order Conformal Weyl Gravity (CWG) framework to determine if observational signatures can uniquely identify the theory.

Methodology
The authors analyze a charged, rotating de Sitter black hole solution within Conformal Weyl Gravity (CWG), immersed in a cold, non-magnetized, pressureless plasma.

Spacetime Model: The study utilizes the exact rotating charged de Sitter solution in CWG, characterized by a radial metric function $\Delta_r$ containing a distinctive charge term proportional to $q^2 r^3 / (6M)$ . This contrasts with the Kerr-Newman-de Sitter (KNdS) solution in GR, where the charge contribution appears as a constant $q^2$ term in $\Delta_r$ (entering quadratically as $q^2$ but without the $r^3$ radial dependence).
Plasma Model: A separable plasma profile is introduced into the Hamilton-Jacobi formalism. The plasma frequency is modeled as $\omega_p^2(r, \theta) = [f_r(r) + f_\theta(\theta)]/\rho^2$ , allowing for analytical tractability of photon geodesics in a dispersive medium.
Observables:
- Photon Region: Equations of motion are derived to find circular photon orbits and the effective potentials.
- Deflection Angle: The finite-distance deflection angle is calculated for observers at finite radii, accounting for the asymptotically de Sitter nature of the spacetime (which precludes the standard spatial infinity approximation).
- Shadow Geometry: Using a local tetrad formalism, the shadow boundary is projected onto the sky of a finite observer. Dimensionless screen coordinates ( $X, Y$ ) are used to compute the effective shadow radius ( $R_s$ ) and distortion ( $\delta_s$ ).
- Emission: The high-energy emission rate is estimated based on the geometric-optics approximation, linking the absorption cross-section to the shadow area.
Constraints: The calculated dimensionless shadow radii are compared against EHT-inferred size intervals for Sgr A* and M87* to derive joint constraints on the charge ( $q$ ) and plasma strength ( $x = \omega_c^2/\omega_0^2$ ).

Key Contributions and Results

Distinctive Charge Response: The most significant finding is the opposite dependence of the shadow size on the charge parameter $q$ between CWG and GR.
- In CWG, increasing the charge $q$ enlarges the black hole shadow. This is a direct consequence of the $q^2 r^3$ term in the radial metric function, which alters the horizon structure and photon region differently than in GR.
- In GR (Kerr-Newman), increasing the charge $q$ reduces the shadow size.
- This qualitative difference persists even in the presence of plasma, offering a potential observational discriminator between the theories.
Plasma Effects: Increasing the plasma strength generally reduces the shadow radius, the signed deflection angle, and the energy emission peak in both theories. While plasma modifies the overall scale of the shadow, it does not erase the qualitative distinction caused by the charge term. The plasma influence is filtered through the background geometry, meaning the same plasma profile produces different signatures in CWG compared to GR.
Deflection Angle Behavior: The finite-distance deflection angle in CWG exhibits a stronger dependence on charge and plasma than in GR. Notably, for high charge values in CWG, the deflection angle can become negative (indicating a reversal in the bending direction relative to the standard lensing geometry), a behavior not observed in the GR cases studied.
Joint Constraints from EHT:
- The study maps the compatibility of the $(q, \text{plasma})$ parameter space with EHT data.
- Because plasma reduces the shadow size in both theories, but charge increases the shadow size in CWG while decreasing it in GR, the interplay between these parameters creates opposite degeneracies.
- In CWG, plasma offsets the shadow enlargement caused by charge; therefore, stronger plasma allows for higher charge values to remain consistent with observed shadow sizes, resulting in an upward-sloping boundary for the maximum allowed charge.
- In GR, both plasma and charge work in the same direction to reduce the shadow size. Consequently, as plasma strength increases, the maximum allowed charge decreases to satisfy the shadow size limit, resulting in a downward-sloping boundary.
- For Sgr A*, the maximum allowed charge in CWG increases from $3.83 \times 10^{-6}$ in vacuum to $1.20 \times 10^{-5}$ at maximum plasma strength, whereas the GR bound decreases from $0.753$ to $0.368$.

Significance and Claims
The paper claims that while plasma effects can mimic shifts in shadow size, the distinct response of the shadow radius to the charge parameter in Conformal Weyl Gravity provides a potential observational route for separating conformal gravity signatures from environmental propagation effects. The authors emphasize that shadow constraints on non-Kerr metrics are incomplete without including the plasma profile as part of the spacetime optics model.

The work demonstrates that the specific radial dependence of the charge term in CWG ( $q^2 r^3$ ) fundamentally alters the lensing and shadow observables compared to GR. By analyzing the joint charge-plasma constraints, the study suggests that future high-precision measurements of black hole shadows, when combined with models of the surrounding plasma, could test the validity of fourth-order conformal gravity against General Relativity. The authors remain modest, noting that their bounds are conditional on specific choices of spin, inclination, and observer radius, and that the numerical bounds are theory-specific geometric limits rather than posterior credible intervals on a common physical charge.

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