⚛️ general relativity

Quantum nucleation of black hole mimickers via chaos dominated tunneling

This paper proposes that quantum chaotic dynamics can catalyze multichannel tunneling to dramatically enhance the nucleation of ultracompact black hole mimickers, such as string theoretic black shells, during gravitational collapse.

Original authors: Ulf Danielsson, Suvendu Giri, Vyshnav Mohan, Larus Thorlacius

Published 2026-07-07

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CC BY 4.0

Original authors: Ulf Danielsson, Suvendu Giri, Vyshnav Mohan, Larus Thorlacius

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 Question: Can Stars Become "Fake" Black Holes?

Imagine a star collapsing under its own gravity. Usually, we think it will crush down until it becomes a black hole—a point of infinite density surrounded by an event horizon (a point of no return).

But some physicists wonder: What if, instead of becoming a black hole, the star collapses into a black hole mimicker? These are ultra-dense objects that look and act almost exactly like black holes from the outside, but they have no event horizon and no singularity. They are like a "fake" black hole that is actually a solid, albeit incredibly strange, shell.

The problem is: How does this happen?
To turn a collapsing star into a mimicker, the matter has to "tunnel" through a massive energy barrier. In quantum mechanics, tunneling is like a ghost walking through a wall. Usually, this is incredibly rare and slow, especially for something as huge as a star. The odds are so low that it seems impossible for a mimicker to form before a black hole does.

The Old Idea: Counting States (And Why It Fails)

Previously, scientists argued that because these mimickers have a huge number of internal "states" (ways the particles inside can be arranged), the odds of forming one should go up. It's like saying, "If I have a billion different lottery tickets, I'm bound to win."

The authors of this paper say: No, that's not how it works.
They use an analogy of an atom inside a giant, noisy shell. Even if the shell has a billion ways to vibrate (high entropy), the atom still has to emit a photon to escape. The sheer number of options in the shell doesn't make the atom decay faster. The "bottleneck" is the connection between the atom and the shell, not the number of states in the shell.

The New Idea: Chaos Dominated Tunneling (CDT)

The authors propose a new mechanism called Chaos Dominated Tunneling (CDT). Instead of just having many options, the system needs many active pathways that work together.

The Analogy: The Crowded Party vs. The Mosh Pit

The Old Way (Simple Tunneling): Imagine trying to walk through a solid wall. You are one person, and the wall is solid. You have a tiny chance of phasing through it.
The "Many States" Way (That doesn't work): Imagine you are a person with a billion different outfits. You still have to walk through the wall alone. Having more outfits doesn't help you pass through the wall.
The CDT Way (Chaos): Imagine you are part of a massive, chaotic mosh pit at a concert. Everyone is pushing, shoving, and interacting randomly. Because there are so many people interacting chaotically, the "wall" of people suddenly opens up a thousand different doors at once.

In this paper, the "wall" is the energy barrier preventing the star from becoming a mimicker. The "people" are the internal degrees of freedom (the tiny quantum parts) of the star.

How It Works: The "Bright Channels"

The authors do some math with particles that have many internal states (like a particle with many different "colors" or "flavors").

The Barrier: Normally, the particle hits a wall it can't cross.
The Chaos: If the internal parts of the particle interact in a chaotic, random way (like a complex, messy dance), something magical happens.
The Result: The chaos creates a huge number of "bright channels." Think of these as open doors. Instead of one tiny door where the particle has to squeeze through, the chaos opens up thousands of doors.
The Outcome: The particle doesn't just have a tiny chance of getting through; it has a very high chance because there are so many open paths. The "exponential suppression" (the thing that makes tunneling impossible) disappears.

They call this Chaos Dominated Tunneling because the chaotic interactions are the main reason the tunneling becomes possible.

Applying It to the "Black Shell"

The authors apply this to a specific type of mimicker called an AdS Black Shell (a shell made of string theory materials).

The Setup: A shell of matter collapses. Inside, it wants to become a "Black Shell" (a stable, horizonless object).
The Barrier: To do this, it must tunnel through a region where classical physics says it can't go.
The Solution: Because the shell has a massive number of internal states (it's huge and complex), and because these states interact chaotically (scrambling information quickly, which is what makes a black hole "black"), the CDT mechanism kicks in.
The Result: The tunneling probability skyrockets. The shell can "nucleate" (pop into existence) much more easily than we thought. The chaotic interactions effectively lower the wall so much that the shell can walk right through it.

What About Locality? (Does this break the laws of physics?)

A common worry is that if a black shell appears instantly at the size of a black hole, it violates "locality" (the idea that things only affect their immediate surroundings). It looks like magic: the center of the star suddenly "knows" it's about to collapse and tunnels out.

The authors explain that this is just quantum tunneling.

The Analogy: Imagine a particle tunneling through a wall. It seems like it disappears on one side and reappears on the other instantly. But you can't use this to send a message faster than light. You can't control when it happens.
The Reality: The "collapse" of the star into a shell isn't a sudden, controlled event. It's a quantum superposition. The star exists in a fuzzy state of "collapsing" and "tunneling" at the same time. An observer inside the star gets "entangled" with this process. They can't use it to send a signal to the outside. The universe remains consistent; it just looks weird from the outside.

The Bottom Line

This paper argues that black hole mimickers are much more likely to form than we thought.

The key is chaos. If the internal parts of the collapsing object interact in a chaotic, complex way, they create a massive number of "open doors" (bright channels) for the object to tunnel through the energy barrier. This "Chaos Dominated Tunneling" makes the formation of these horizonless objects a viable, even probable, outcome of gravitational collapse, offering a potential alternative to the traditional black hole.

Technical Summary: Quantum Nucleation of Black Hole Mimickers via Chaos Dominated Tunneling

1. The Problem
Black hole mimickers—ultracompact, horizonless objects proposed as alternatives to black holes in various extensions of general relativity and beyond-Standard-Model scenarios—face a significant formation hurdle. For such objects to form via gravitational collapse, the system must undergo a quantum mechanical tunneling event across a potential barrier on the scale of the Schwarzschild radius. Standard tunneling probabilities are exponentially suppressed, making the nucleation of these objects highly unlikely.

Previous arguments for the viability of mimickers (e.g., fuzzballs, frozen stars, AdS black shells) have relied on the heuristic that the large entropy of the final state compensates for this suppression. However, the authors argue that a large number of final states alone does not necessarily increase the tunneling rate. As demonstrated by the analogy of an excited atom decaying into a macroscopic shell, the decay rate is determined by the coupling strength, not merely the number of available states; the effective coupling to each state is diluted by the square root of the number of degrees of freedom ( $N$ ), leaving the total rate unchanged ( $g^2 \to N \times (g/\sqrt{N})^2 = g^2$ ). To achieve a viable formation mechanism, the system requires not just a large number of states, but a large number of available channels where the transition proceeds without exponential suppression.

2. Methodology
The paper employs a two-pronged approach: first, a theoretical construction of quantum mechanical models demonstrating "multichannel enhancement," and second, the application of this mechanism to the specific case of an AdS black shell nucleating during gravitational collapse.

Quantum Mechanical Models: The authors analyze a non-relativistic particle with $N$ internal degrees of freedom tunneling through a potential barrier. The dynamics are governed by a Schrödinger equation where the potential includes an interaction matrix coupling the internal states. They examine three specific cases:
1. Square Barrier with Uniform Coupling: A matrix with uniform off-diagonal couplings ( $-g$ ) and diagonal barrier height ( $V_0$ ). This yields one "bright" channel (an eigenvector with eigenvalue $V_0 - (N-1)g$ ) and $N-1$ "dark" channels. If $(N-1)g > V_0$ , the barrier for the bright channel vanishes, removing exponential suppression. However, the projection of the initial state onto this single channel introduces a $1/N$ suppression factor.
2. Circulant Matrices: To overcome the $1/N$ projection suppression, the authors utilize Hermitian circulant matrices. By tuning coupling coefficients, they demonstrate that a finite fraction of eigenvalues can become negative (or sufficiently small), creating an $O(N)$ number of "bright channels." This ensures the total transmission is not exponentially suppressed.
3. Wigner Random Matrices: The authors consider coupling matrices of the form $M = V_0 I - gJ$ , where $J$ is a random matrix. Citing Wigner's semicircle law, they show that for large $N$ , a finite fraction of eigenvalues becomes negative if $2\sigma g \sqrt{N} > V_0$ . This scenario, driven by chaotic interactions, is identified as the most robust mechanism.
Application to AdS Black Shells: The authors apply these findings to the nucleation of a string-theoretic AdS black shell. They model the shell as a thin shell in 4D general relativity with an effective Hamiltonian constraint derived from Israel's junction conditions. The Hamiltonian is non-quadratic in momentum, involving a $\cosh(G_4 p/r)$ term, which implies area quantization. They analyze the tunneling of a bubble of AdS vacuum from $r=0$ to a critical radius $r_0$ within a collapsing matter shell. The tunneling trajectory is truncated when the nucleating shell encounters the collapsing matter at radius $R$ .

3. Key Contributions and Results

Chaos Dominated Tunneling (CDT): The paper introduces and defines "Chaos Dominated Tunneling" (CDT) as a mechanism distinct from the known "Chaos Assisted Tunneling" (CAT). While CAT lowers a barrier via chaotic interactions, CDT posits that in systems with an enormous number of internal states (like black shells), chaotic interactions (modeled by random matrices) open up an $O(N)$ number of bright channels. This effectively overwhelms the original exponential suppression of the tunneling barrier.
Multichannel Enhancement Proof: The authors provide a theoretical proof of principle that a complex object with coherent internal degrees of freedom can tunnel more easily than a simple one. Specifically, they show that if the interaction matrix possesses $O(N)$ negative eigenvalues, the transmission coefficient is no longer exponentially suppressed.
Enhanced Nucleation Probability: Applying CDT to the AdS black shell, the authors argue that the chaotic dynamics of the shell's internal degrees of freedom (required for rapid information scrambling) displace energy eigenvalues such that the effective Euclidean momentum for a large fraction of channels approaches zero. This allows the shell to tunnel through the classically forbidden region without the usual exponential suppression.
Resolution of Locality Concerns: The paper addresses the apparent non-locality of a black shell suddenly appearing at the Schwarzschild radius. It argues that because the process is a stochastic quantum tunneling event, it does not violate locality. An observer inside the collapsing cloud becomes entangled with the shell, resulting in a macroscopic superposition of tunneling times. No information can be transmitted faster than light, as the exact time of tunneling cannot be controlled or predicted by the observer.

4. Significance and Claims
The paper claims to provide a concrete microscopic underpinning for the formation of black hole mimickers, moving beyond heuristic entropy arguments. By identifying CDT as a viable mechanism, the authors suggest that the nucleation of black shells during gravitational collapse is not exponentially suppressed, thereby making these objects a physically plausible alternative to black holes.

The authors explicitly state that while they have demonstrated that the suppression is removed, they have not yet proven that the formation probability of a black shell exceeds that of a standard black hole. They posit that since the entropy of a black shell ( $S_{shell}$ ) drastically exceeds that of a black hole ( $S_{bh}$ ) at a given energy, the number of bright channels ( $N \sim e^{S_{shell}}$ ) should overwhelm the contribution from black hole microstates ( $e^{S_{bh}}$ ), making the shell the more probable end product. However, they defer the detailed computation of this transition amplitude to future work.

The paper concludes that CDT legitimizes the possibility of black shell nucleation, provided the system possesses the requisite chaotic dynamics and a large number of internal degrees of freedom, which are expected features of macroscopic many-body systems in quantum gravity.