⚛️ general relativity

Circular orbits and observational features of the rotating Simpson-Visser black hole surrounded by a thin accretion disk

This paper systematically investigates the radiative properties and optical appearance of rotating Simpson-Visser black holes with thin accretion disks, demonstrating that while the regularization parameter $g$ suppresses radiative flux and intensity while widening the photon ring, it leaves radiative efficiency unchanged compared to Kerr black holes, thereby offering distinct observational signatures for future high-resolution tests.

Original authors: Ziyang Li, Shou-Qi Liu, Jia-Hui Huang

Published 2026-02-17

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CC BY 4.0

Original authors: Ziyang Li, Shou-Qi Liu, Jia-Hui Huang

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

The Big Picture: Hunting for "Smooth" Black Holes

Imagine you are a detective trying to solve a mystery about the universe's most dangerous traps: Black Holes.

For a long time, our best theory (General Relativity) told us that if you fall into a black hole, you eventually hit a "singularity"—a point where the math breaks down, density becomes infinite, and physics stops making sense. It's like a pothole in the road so deep it swallows your car and disappears.

But some physicists think, "That can't be right. Nature probably doesn't do infinite potholes." They propose Regular Black Holes. These are like black holes that have been "smoothed out." Instead of a sharp, infinite spike in the middle, they have a gentle, round core. Think of it as replacing a jagged, broken glass shard with a smooth, polished marble.

One specific model for this "smooth" black hole is called the Simpson-Visser (SV) black hole. It has a special "knob" (called parameter $g$ ) that controls how smooth the center is. If the knob is off, it's a normal black hole. If you turn the knob up, the center gets smoother, and if you turn it all the way up, it might even turn into a wormhole (a tunnel to another place).

The Problem: They Look Exactly the Same

The Event Horizon Telescope (EHT) took pictures of two famous black holes, Sgr A* and M87*. These pictures show a dark circle (the "shadow") surrounded by a ring of light.

The problem? The SV black holes are master of disguise.

The Shadow Trick: If you only look at the size and shape of the dark shadow, an SV black hole looks exactly like a standard spinning black hole (called a Kerr black hole). It's like trying to tell the difference between a real apple and a perfect wax apple just by looking at their silhouettes in the dark. You can't do it.

The Solution: Listen to the "Music" of the Accretion Disk

Since the shadow doesn't give it away, the authors of this paper decided to look at the accretion disk.

The Analogy: Imagine the black hole is a giant whirlpool. The water swirling around it (the accretion disk) gets super hot and glows.
The authors asked: "If the center of the whirlpool is smooth (SV) instead of jagged (Kerr), does the water swirl differently? Does it glow with a different color or intensity?"

They ran massive computer simulations to see how the "smoothness knob" ( $g$ ) changes the light we see.

What They Found (The Detective's Clues)

Here are the main discoveries, explained simply:

1. The "Efficiency" is the Same

The Analogy: Imagine a water wheel. How much energy does it get from the water falling?
The Result: Surprisingly, whether the black hole is "smooth" or "jagged," the amount of energy it extracts from the falling matter is identical. The "smoothness" doesn't change the overall efficiency of the engine.

2. The "Brightness" Changes

The Analogy: Think of the accretion disk as a campfire.
The Result: When the "smoothness knob" ( $g$ ) is turned up, the fire burns less brightly. The peak temperature and the total light emitted drop slightly. It's like the smooth center makes the swirling gas a little less turbulent, so it doesn't get as hot at its hottest point.

3. The "Ring" Gets Wider

The Analogy: Look at the ring of light around the black hole shadow.
The Result: As the black hole gets smoother, the ring of light gets wider. It's like the "halo" around the shadow expands. This is a crucial clue! If we can measure the width of that ring very precisely, we might be able to tell if the black hole is "smooth" or "jagged."

4. The "Redshift" (Color Shift)

The Analogy: Imagine a siren passing you. As it moves away, the sound gets lower (redshift). As it moves toward you, it gets higher (blueshift). Light does the same thing near a black hole.
The Result: The "smoothness" changes how the light shifts colors. Specifically, it makes the "blueshifted" (brighter) parts of the image slightly more intense, especially if you are looking at the black hole from a steep angle.

Why This Matters

The paper concludes that while the shadow (the dark hole) is a liar and hides the truth, the accretion disk (the glowing ring) is a truth-teller.

The Takeaway: If we want to know if black holes have "smooth" centers (no singularities) or if they are the "jagged" ones predicted by Einstein, we shouldn't just measure the size of the shadow. We need to look at the brightness, temperature, and width of the light ring surrounding it.

The Future

The authors suggest that future telescopes (which will be even sharper than the EHT) should look for these subtle differences. If we see a wider ring or a specific dimming pattern, it could be the first proof that black holes don't have infinite singularities, but rather a smooth, regular core.

In short: The black hole is wearing a mask (the shadow), but its voice (the light from the disk) is starting to give it away. We just need to listen closely enough.

1. Problem Statement

The Event Horizon Telescope (EHT) has provided horizon-scale images of supermassive black holes (Sgr A* and M87*), confirming General Relativity (GR) in the strong-gravity regime. However, GR predicts spacetime singularities, which are physically problematic. Regular black holes (like the Simpson–Visser or SV metric) have been proposed to resolve these singularities by replacing the central singularity with a regular core or throat.

A critical challenge arises in distinguishing these regular black holes from standard Kerr black holes using current observational data. Previous studies have shown an intrinsic degeneracy: for rotating SV black holes with a small regularization parameter ( $g$ ), the shadow size and shape are theoretically identical to those of a Kerr black hole with the same mass and spin. Consequently, shadow imaging alone cannot constrain the regularization parameter $g$ . The authors aim to break this degeneracy by investigating accretion disk-related observables (radiative properties and optical appearance) which may be more sensitive to the near-horizon geometry modifications introduced by $g$ .

2. Methodology

The study employs a combination of analytical calculations and numerical simulations within the framework of the rotating Simpson–Visser metric.

Metric and Geometry: The authors utilize the rotating SV metric (derived via a modified Newman–Janis algorithm), characterized by mass $M$ , spin $a$ , and a regularization parameter $g$ . They analyze the event horizon structure and classify the spacetime into regular black holes, single-horizon black holes, and traversable wormholes based on $g$ .
Geodesic Analysis: They derive the equations of motion for massive test particles on equatorial circular orbits. Key quantities calculated include specific energy ( $E$ ), angular momentum ( $L$ ), angular velocity ( $\Omega$ ), and the radius of the Innermost Stable Circular Orbit (ISCO).
Radiative Modeling: Using the Novikov–Thorne thin-disk model, they calculate:
- Radiative flux ( $F$ ) and effective temperature ( $T_{\text{eff}}$ ).
- Spectral luminosity ( $\nu L_\nu$ ) for distant observers, incorporating gravitational redshift.
- Specific astrophysical parameters for Sgr A* and M87* are used to generate concrete physical predictions.
Ray-Tracing Simulations: A backward ray-tracing technique is employed to simulate the optical appearance of the black hole. This involves tracing photon trajectories from an observer's screen to the accretion disk to determine:
- Observed specific intensity ( $I_{\text{obs}}$ ).
- Redshift factor distributions ( $g_n$ ) for direct, lensed, and higher-order images.
- Flux distributions across the observer's screen.

3. Key Contributions and Results

A. Orbital Dynamics and Radiative Efficiency

ISCO Dependence: The ISCO radius decreases monotonically as the regularization parameter $g$ increases (for prograde orbits).
Degeneracy Breaking: While $g$ affects the radial profiles of $E$ , $L$ , and $\Omega$ , the values of these quantities evaluated specifically at the ISCO remain independent of $g$ .
Radiative Efficiency: Consequently, the radiative efficiency ( $\eta$ ) of the rotating SV black hole is identical to that of a Kerr black hole with the same spin. This implies that total energy conversion efficiency cannot distinguish between the two models.

B. Radiative Properties of the Accretion Disk

Although efficiency is unchanged, local radiative properties are sensitive to $g$ :

Flux and Temperature: The regularization parameter $g$ $g$ suppresses the peak values of the dimensionless radiative flux ( $F_*$ $F_{*}$ ) and effective temperature ( $T^*_{\text{eff}}$ $T_{eff}^{*}$ ).
- Example (Sgr A):* For $a=0.5$ and $g=1.86$ , the peak flux is $\approx 4\%$ lower than the Kerr case ( $g=0$ ).
- Example (M87):* For $a=0.8$ and $g=1.5$ , the peak flux is $\approx 6\%$ lower.
Spectral Luminosity: The spin parameter $a$ significantly enhances spectral luminosity, while the effect of $g$ is weaker but measurable. For $a=0.5$ , the Kerr black hole's peak spectral luminosity is approximately 1.01 times that of the SV black hole with $g=1.86$ .

C. Optical Appearance and Ray-Tracing

Shadow and Photon Ring: As $g$ increases, the size of the inner shadow (event horizon projection) decreases, while the width of the photon ring (the bright luminous curve) increases.
Observed Intensity: The overall observed intensity is significantly suppressed by increasing $g$ .
Redshift and Asymmetry:
- At high inclination angles, Doppler effects create asymmetry (brighter blueshifted side, dimmer redshifted side).
- Increasing $g$ enhances the blueshifted regions in both direct and lensed images at high inclinations, increasing the intensity contrast.
- The photon ring region becomes broader with larger $g$ , suggesting that high-resolution observations of ring structures could be a key discriminator.

4. Significance

Breaking the Degeneracy: The paper demonstrates that while shadow size cannot distinguish rotating SV black holes from Kerr black holes, accretion disk observables (specifically peak flux, temperature, and photon ring width) provide a viable avenue to break this degeneracy.
Observational Guidance: The results suggest that future high-resolution observations (beyond current EHT capabilities) focusing on the photon ring width and intensity profiles of high-spin, high-inclination black holes could constrain the regularization parameter $g$ .
Theoretical Implications: The findings offer a pathway to test the "regular black hole" hypothesis against the standard Kerr hypothesis, potentially providing evidence for the existence of singularity-free spacetimes and constraining modifications to General Relativity in the strong-field regime.

Conclusion

The study concludes that while the global radiative efficiency remains unchanged, the local radiative flux, effective temperature, and detailed optical appearance (intensity profiles and photon ring width) are sensitive to the regularization parameter $g$ . These features offer critical theoretical guidance for distinguishing rotating Simpson–Visser black holes from Kerr black holes in future astrophysical observations.