5D Rotating Black Holes as dark matter in Dark Dimension Scenario: Hawking Radiation versus the Memory Burden Effect

This paper proposes that five-dimensional primordial rotating black holes, whose lifetimes are significantly extended by the "dark dimension" scenario and the memory burden effect, can survive to the present day and potentially account for all of the universe's dark matter.

The Gist

The Big Picture: A New Kind of Dark Matter

Imagine the universe is like a giant, invisible soup called Dark Matter. Scientists know it's there because it holds galaxies together, but they can't see it. For decades, one leading theory was that this soup is made of tiny, ancient black holes formed right after the Big Bang, called Primordial Black Holes (PBHs).

However, there's a problem. In our normal 4-dimensional world (3 dimensions of space + 1 of time), these tiny black holes should have "boiled away" and disappeared billions of years ago due to a process called Hawking Radiation. It's like a cup of hot coffee left on a table; eventually, it cools down and evaporates. If these black holes evaporated, they can't be the dark matter holding our universe together today.

This paper proposes a solution: What if our universe has a secret, hidden dimension?

The Setting: The "Dark Dimension"

The authors use a theoretical idea called the "Dark Dimension" scenario. Think of our universe not as a flat sheet of paper, but as a sheet of paper with a tiny, rolled-up tube attached to it. This tube is a fifth dimension, but it's incredibly small—about the width of a human hair (a few micrometers).

In this scenario, gravity can leak into this tiny tube, but the other forces (like light and electricity) are stuck on the flat sheet. This changes the rules of the game for black holes.

The Main Characters: Spinning Black Holes

The paper focuses on rotating black holes. Imagine a figure skater spinning on ice.

1. The Spin-Down Phase: As the black hole radiates energy (like the skater sweating), it loses its spin. The paper calculates that during this phase, the black hole loses about 50% to 60% of its mass. It's like the skater losing a heavy backpack while spinning, but the act of spinning actually helps them hold onto the rest of their weight longer than expected.
2. The Result: After losing its spin, the black hole becomes a "Schwarzschild" black hole (a non-spinning, round one).

The Twist: The "Memory Burden"

Here is the most creative part of the paper. The authors introduce a concept called the "Memory Burden Effect."

Imagine the black hole is a sponge. As it evaporates, it doesn't just lose water; it also tries to "remember" everything it ever swallowed.

• The Analogy: Think of the black hole as a library. As books (matter) are removed, the librarian (the black hole) has to keep a record of every book that ever entered. The more books it has "lost," the heavier the mental load becomes.
• The Effect: Eventually, this "mental load" (information) becomes so heavy that the black hole gets "stuck." It becomes too tired to evaporate any further. The radiation slows down dramatically, almost stopping.

In the paper's terms, this "memory burden" acts like a brake pedal on the evaporation process. Instead of boiling away completely, the black hole enters a stable state where it survives for trillions of years.

The Conclusion: Why This Matters

The authors ran the numbers for these 5-dimensional, spinning black holes:

1. Slower Evaporation: Because of the extra dimension, the black holes lose heat much slower than they would in our normal 4D world.
2. The Brake: The "Memory Burden" hits the brakes even harder, stopping the evaporation process entirely for smaller black holes.

The Result:
Black holes that would have vanished in a normal universe (those weighing less than a mountain) can actually survive until today if they live in this "Dark Dimension" and carry a heavy "memory burden."

The paper concludes that these surviving, ancient, spinning black holes could be the missing Dark Matter that makes up the entire universe. They are the "ghosts" that never left the party because the extra dimension and their own "memory" kept them alive.

Summary in One Sentence

By adding a tiny hidden dimension and a "memory weight" that slows down evaporation, this paper suggests that tiny, spinning black holes from the dawn of time could still be floating around today, making up all the dark matter in the universe.

Technical Summary

Technical Summary: 5D Rotating Black Holes as Dark Matter in the Dark Dimension

Problem Statement
Standard four-dimensional (4D) cosmology faces significant challenges in identifying viable primordial black hole (PBH) candidates for dark matter (DM). In a 4D framework, PBHs with masses $M \lesssim 5 \times 10^{14}$ g would have completely evaporated via Hawking radiation by the present epoch, while those in the range $10^{15} \text{ g} \lesssim M \lesssim 10^{17}$ g are severely constrained by extragalactic gamma-ray backgrounds. Consequently, 4D PBHs cannot account for the entirety of the observed dark matter density.

This work addresses this limitation within the "Dark Dimension" scenario, a theoretical framework derived from the Swampland Program. This scenario posits a single extra dimension compactified at a micron scale ($R_C \sim \mu$m), which correlates the smallness of the dark energy scale ($\Lambda$) with the size of the extra dimension. The central question is whether 5D rotating primordial black holes, subject to the modified gravitational dynamics of this extra dimension and the "memory burden" effect, can survive to the present day and constitute the dominant form of dark matter.

Methodology
The authors employ a multi-stage analytical approach to model the evolution and lifetime of 5D rotating black holes:

1. Theoretical Framework: The analysis assumes a 5D spacetime ($D=4+1$) where the Standard Model fields are confined to a 3-brane, while gravity propagates in the bulk. The black holes are modeled as Myers-Perry solutions with a single rotation parameter aligned with the brane.
2. Greybody Factor Calculation: The authors compute the greybody factors ($\Gamma_{s,\ell,m}$) for fields of spin $s=0, 1/2, 1$ propagating on the brane. Using a low-frequency expansion and matching near-horizon and far-field solutions (via hypergeometric functions), they derive the absorption probabilities necessary to calculate the Hawking radiation spectrum.
3. Coupled Evolution Equations: The mass ($M$) and angular momentum ($J$) evolution are treated as a coupled system. The authors derive an analytical relation $M(J)$ by eliminating the time variable, allowing them to track the "spin-down" phase where the black hole loses angular momentum before transitioning to a non-rotating Schwarzschild phase.
4. Lifetime Integration: The total lifetime is calculated in two distinct phases:
   • Spin-down Phase: The duration required for the black hole to lose its angular momentum.
   • Schwarzschild Phase: The subsequent evaporation of the resulting non-rotating black hole.
5. Memory Burden Effect: The study incorporates the "memory burden" effect (proposed by Dvali), a quantum mechanical mechanism where the accumulation of quantum information (memory) on the black hole horizon creates an energy barrier that suppresses the Hawking radiation rate once a critical fraction of the mass is lost. This is modeled by modifying the mass loss rate with an entropy-dependent factor $1/S^p$.

Key Contributions and Results

• Suppressed Hawking Radiation in 5D: The analysis confirms that in the Dark Dimension scenario ($n=1$), the Hawking temperature is lower, and the radiation rate is significantly suppressed compared to 4D counterparts. This suppression arises because the horizon radius is larger for a given mass in higher dimensions, leading to a reduced emission power ($P \propto T^2$).
• Spin-Down Dynamics: The authors find that during the spin-down phase, a 5D rotating black hole loses approximately 40% to 60% of its initial mass before its angular momentum vanishes. This phase lasts on the order of $O(10^9)$ years.
• Extended Survival Mass Window: Due to the suppressed radiation, the minimum mass required for a PBH to survive until the present day is lowered. In the standard 5D scenario (without memory burden), PBHs with initial masses $M \gtrsim 10^{10}$ g can survive, whereas in 4D, the limit is $\sim 10^{15}$ g.
• Impact of the Memory Burden Effect: The inclusion of the memory burden effect dramatically alters the evaporation timeline. For specific values of the exponent $p$ (governing the non-linearity of the interaction), the evaporation rate is exponentially suppressed after the black hole loses a critical fraction of its mass.
  • For $p=2$, the semi-classical description breaks down, and the black hole transitions to a long-lived remnant phase.
  • This effect allows even lighter PBHs (potentially below $10^8$ g) to avoid complete evaporation, effectively stabilizing them against the constraints of Big Bang Nucleosynthesis (BBN) and gamma-ray backgrounds.

Significance and Claims
The paper claims that 5D rotating primordial black holes are compelling candidates for the totality of dark matter in the universe. The significance of this work lies in two main mechanisms:

1. Geometric Suppression: The existence of a micron-scale extra dimension naturally suppresses Hawking radiation, extending the lifetime of lighter PBHs that would otherwise be excluded in 4D models.
2. Quantum Stabilization: The memory burden effect provides a mechanism to further prolong the lifetime of these black holes, potentially allowing them to persist as stable relics.

The authors conclude that the combination of the Dark Dimension scenario and the memory burden effect resolves the tension between PBH evaporation constraints and the requirement for a dark matter component, suggesting that rotating higher-dimensional PBHs could constitute 100% of the observed dark matter density.