Memory burden effect of regular primordial black holes

This paper demonstrates that combining regular primordial black hole metrics with the memory burden effect significantly suppresses Hawking radiation, thereby opening a new mass window of $10^6$--$10^8$ g where such black holes can constitute all dark matter without violating Big Bang nucleosynthesis constraints.

The Gist

The Big Mystery: What is Dark Matter?

Imagine the universe is a giant puzzle. We can see the pieces that make up stars, planets, and us (about 27% of the puzzle), but the rest is missing. Scientists call this missing piece Dark Matter. We know it's there because it has gravity, but we can't see it.

For a long time, scientists thought Dark Matter was made of invisible, tiny particles (like "ghost particles"). But after decades of searching, we haven't found any. So, scientists are looking at other ideas. One popular idea is that Dark Matter is made of Primordial Black Holes (PBHs). These aren't the black holes formed by dying stars; they are tiny black holes that formed in the very first split-second of the universe.

The Problem: The "Vanishing Act"

There's a big problem with the PBH idea. According to standard physics (Hawking Radiation), tiny black holes are like ice cubes in a hot room: they evaporate.

• If a black hole is too light (smaller than a mountain), it should have completely evaporated billions of years ago.
• This means the "small" black holes we need to explain Dark Matter shouldn't exist today. They would have vanished.

The Solution: Two "Magic Shields"

This paper suggests a way to save these tiny black holes. The authors combine two theoretical ideas that act like shields, slowing down the evaporation process so the black holes can survive until today.

Shield #1: The "Smoothie" Black Holes (Regular Black Holes)

Standard black holes are described as having a "singularity"—a point in the center where physics breaks down and density becomes infinite. It's like a glitch in a video game.

• The Paper's Idea: The authors use "Regular Black Holes." Imagine a standard black hole is a sharp, jagged rock. A Regular Black Hole is like that same rock, but smoothed out into a perfect, round ball. There is no sharp point in the center.
• The Effect: Because the center is "smooth," the black hole is cooler. A cooler black hole radiates heat (evaporates) much slower than a hot, jagged one. This gives the black hole a bit more time to live.

Shield #2: The "Backpack" Effect (Memory Burden)

This is the second, more powerful shield.

• The Analogy: Imagine a black hole is a person walking down a hallway. As they walk, they drop papers (radiation/energy) behind them. In standard physics, they drop papers at a steady, fast pace.
• The Twist: The "Memory Burden" idea says that as the black hole loses mass, it has to carry a heavy "backpack" of information about its past. The more it loses, the heavier the backpack gets.
• The Result: Eventually, the backpack gets so heavy that the black hole gets tired and slows down. It stops dropping papers as fast. This "Memory Burden" acts like a brake, drastically slowing down the evaporation rate once the black hole has lost half its weight.

Putting It Together: The New "Safe Zone"

The authors combined these two shields (the Smoothie shape + the Heavy Backpack) and tested three different mathematical models for these smooth black holes (named after scientists Hayward, Bardeen, and Simpson-Visser).

What they found:

1. The "Sweet Spot": When you use both shields, tiny black holes that were previously thought to be impossible (too small to survive) can actually live until today.
2. The New Mass Window: They found a new range of sizes where these black holes could make up 100% of Dark Matter. This range is between 1 million and 100 million grams (roughly the weight of a large car to a small truck).
3. The "Big Bang" Test: The universe went through a hot, chaotic phase called Big Bang Nucleosynthesis (BBN) where the first atoms were formed. If black holes evaporate too fast during this time, they mess up the recipe for atoms (creating too much Helium or destroying Deuterium).
   • The authors checked this and found that because these black holes are so slow to evaporate (thanks to the two shields), they don't mess up the recipe. They are "quiet" enough to coexist with the formation of the universe.

The Conclusion

The paper concludes that if we accept these two theoretical ideas (smooth centers and the memory burden), the door is wide open for tiny black holes to be the Dark Matter we've been looking for.

• Without the shields: Tiny black holes vanish instantly.
• With the shields: Tiny black holes (weighing as much as a car) can survive the age of the universe and hide in the dark, explaining the missing mass.

The authors note that while this is a theoretical model (a "toy model" in physics terms), it shows that non-singular black holes are a very promising candidate for solving the Dark Matter mystery.

Technical Summary

Technical Summary: Memory Burden Effect of Regular Primordial Black Holes

Problem Statement
Primordial Black Holes (PBHs) are a leading candidate for non-particle Dark Matter (DM). However, standard Schwarzschild PBHs with masses below $10^{15}$ g are constrained by Hawking radiation to have evaporated completely before the present epoch, excluding them as viable DM candidates in the low-mass regime. While two distinct theoretical mechanisms have been proposed independently to extend the allowed PBH mass window to smaller scales—Regular Black Holes (RBHs) with non-singular metrics and the Memory Burden (MB) effect—this paper addresses the lack of a combined analysis. The authors investigate whether the synergy of these two mechanisms can further relax evaporation constraints and open a new, previously excluded mass window for PBHs to constitute all Dark Matter.

Methodology
The study employs a phenomenological approach within a four-dimensional framework, treating specific RBH metrics as effective toy models. The methodology involves three primary steps:

1. Selection of Regular Metrics: The authors analyze three specific non-singular black hole solutions: the Hayward, Bardeen, and Simpson–Visser metrics. For each, they derive the modified Hawking temperature ($T$) and entropy ($S$) under a "self-similar" evaporation ansatz, where the regularization parameter $\ell$ is proportional to the horizon radius ($R$). This avoids the formation of stable zero-temperature remnants, which would otherwise require infinite time to form.
2. Integration of the Memory Burden Effect: The authors incorporate the MB effect, which posits that as a black hole loses mass, the retention of information regarding its formation history imposes a dynamical cost that suppresses the evaporation rate. They adopt the "swift" MB scenario, where the suppression factor $S^{-k}$ (with $k$ being a strength parameter) is applied only after the black hole has lost a specific fraction ($q=1/2$) of its initial mass ($M_{ini}$).
3. Constraint Analysis: The modified evaporation rates are used to calculate the lifetimes of these regular PBHs. The authors then evaluate the constraints imposed by Big Bang Nucleosynthesis (BBN). They calculate the energy injection from PBH evaporation during the BBN epoch and compare it against background radiation densities to determine the upper limits on PBH abundance ($f_{PBH}$) as a function of initial mass.

Key Contributions and Results

• Combined Suppression Mechanism: The paper demonstrates that while RBHs naturally lower the Hawking temperature compared to singular Schwarzschild black holes (thereby extending lifetimes), the addition of the MB effect provides a secondary, dominant suppression of the evaporation rate once the black hole enters the MB regime.
• New Mass Window: For a benchmark MB strength parameter of $k=1$, the authors identify a new viable mass window for PBHs to constitute 100% of Dark Matter in the range of approximately $10^6$ to $10^8$ g. This range was previously excluded by standard evaporation constraints.
• Convergence of Metrics: A significant finding is that the MB effect effectively washes out the differences between the specific RBH geometries. While the Hayward metric initially shows the strongest suppression due to its temperature profile, the $S^{-k}$ factor in the MB regime dominates the dynamics. Consequently, for $k \ge 1$, the lifetimes and survival thresholds of Hayward, Bardeen, and Simpson–Visser PBHs become nearly identical.
• BBN Constraints: The study finds that for PBHs entering the MB phase prior to the BBN epoch, the radiated energy is sufficiently suppressed such that the BBN constraints on their abundance are negligible. The mass ranges excluded by BBN ($M \lesssim 10^2$ g) are far below the lower mass limits imposed by the requirement that PBHs must survive to the present day ($M \gtrsim 10^6$ g).
• Parameter Dependence: The authors systematically explore the dependence on the MB strength parameter $k$ (ranging from 0.2 to 2.0). They find that as $k$ increases, the lower mass bound for survival decreases further, broadening the allowed window. They also note a non-trivial interplay where the dominant suppression mechanism shifts from metric geometry (at low $k$) to entropy-based suppression (at high $k$), altering which specific RBH model yields the lowest mass bound.

Significance
The paper claims that this work provides a comprehensive phenomenological framework demonstrating that the combination of non-singular black hole geometries and the memory burden effect can theoretically resolve the spacetime singularity problem while simultaneously revitalizing the viability of low-mass PBHs as a Dark Matter candidate. The authors emphasize that their results are model-dependent (relying on the self-similar ansatz and specific metric choices) but compellingly illustrate the potential of non-singular black hole geometries in PBH cosmology. They conclude that the specific mass boundaries depend on the value of $k$, but the existence of a fully open mass window in the $10^6$–$10^8$ g range is a robust feature of the combined model.