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arxiv: 2605.19463 · v1 · pith:S2ZOKONNnew · submitted 2026-05-19 · 🌌 astro-ph.CO

Memory burden effect of regular primordial black holes

Jin-Rong Du , Zi-Zhuo Zhang , Nan Li This is my paper

Pith reviewed 2026-05-20 03:03 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords primordial black holesmemory burden effectregular black holesdark matterHawking evaporationBig Bang nucleosynthesisHayward metricBardeen metric
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The pith

Regular primordial black holes with the memory burden effect can account for all dark matter in the 10^6 to 10^8 gram mass range.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates combining non-singular regular metrics for primordial black holes with the memory burden effect to slow their evaporation. Standard Hawking radiation would cause PBHs lighter than about 10^15 grams to disappear long ago, ruling them out as dark matter. The memory burden kicks in after some mass loss and further reduces the rate at which they radiate away. With this, for a benchmark strength, these black holes in the 10^6 to 10^8 gram range can persist and make up the entire dark matter density without conflicting with nucleosynthesis in the early universe. This matters because it revives a previously excluded range of small black holes as a possible dark matter explanation.

Core claim

By applying a phenomenological self-similar evaporation law that includes the memory burden effect to the Hayward, Bardeen, and Simpson-Visser regular black hole metrics, the evaporation constraints are significantly relaxed. For the MB strength parameter k=1, this opens a new mass window around 10^6--10^8 g in which regular PBHs can constitute all of the dark matter while remaining consistent with Big Bang nucleosynthesis bounds.

What carries the argument

A phenomenological self-similar evaporation law incorporating the memory burden effect after a fraction of the initial mass has been lost, applied to regular non-singular black hole metrics.

If this is right

  • Big Bang nucleosynthesis constraints on evaporating PBHs are relaxed by the combined regular-metric and memory-burden effects.
  • Regular PBHs in the 10^6--10^8 g window can comprise the full dark matter density.
  • The suppression from memory burden operates similarly across the Hayward, Bardeen, and Simpson-Visser metrics.
  • Smaller-mass regular PBHs become viable without evaporating away before the present day.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Microlensing surveys or gravitational-wave detectors could search for PBH populations specifically in this newly viable mass window.
  • If the phenomenological law holds, similar memory-burden suppression might extend the lifetimes of other regular black hole candidates beyond the PBH context.
  • Deriving an evaporation rate from the underlying quantum structure rather than assuming self-similarity would test whether the mass window survives.

Load-bearing premise

The black hole evaporation follows a specific phenomenological self-similar law that incorporates the memory burden effect once a certain mass loss threshold is reached.

What would settle it

A direct first-principles calculation of the evaporation rate from the regular metrics showing no such suppression, or precise light-element abundance measurements that match standard predictions with no allowance for extra radiation from evaporating PBHs in the 10^6-10^8 g range.

read the original abstract

Primordial black holes (PBHs) have attracted intensive research interest as a promising candidate of dark matter. However, because of the Hawking radiation, the PBHs lighter than $10^{15}~\rm{g}$ have already evaporated before today. To extend the PBH mass window to small-mass range, two possible ingredients are explored. The first is the consideration of regular PBHs with non-singular metrics, which can decrease the Hawking temperature, thereby lowering black hole evaporation. The second is the incorporation of the memory burden (MB) effect, which can further suppress the evaporation rate, after regular PBHs have lost a certain amount of their initial masses. In this work, we combine these two ingredients and study the MB effects of three types of regular PBHs (the Hayward, Bardeen and Simpson--Visser black holes). Assuming a phenomenological self-similar evaporation, we find that the MB effect significantly relaxes the evaporation constraints. For a benchmark of the MB strength parameter $k=1$, a new PBH mass window opens at around $10^6$--$10^8$ g, where regular PBHs can compose all dark matter without violating the Big Bang nucleosynthesis bounds.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The manuscript studies the evaporation of primordial black holes (PBHs) using three regular (non-singular) metrics—Hayward, Bardeen, and Simpson-Visser—combined with a memory burden (MB) suppression effect. Assuming a phenomenological self-similar evaporation law that activates MB suppression after a fixed fractional mass loss, the authors report that for benchmark MB strength k=1 the lifetime of PBHs in the 10^6–10^8 g range is sufficiently extended to evade Big Bang nucleosynthesis (BBN) energy-injection bounds, thereby opening a new window in which regular PBHs could constitute all dark matter.

Significance. If the phenomenological evaporation model is accepted, the result would relax existing lower-mass constraints on PBH dark matter and identify a concrete new mass interval. The paper’s explicit numerical comparison across three regular metrics and the direct mapping to BBN bounds constitute a clear, falsifiable prediction. However, the significance is reduced by the absence of a first-principles derivation of the evaporation rate from the metrics’ surface gravity or grey-body factors and by the benchmark status of k=1.

major comments (3)
  1. [§3] §3 (Evaporation model): The self-similar form dM/dt = f(M,k) that incorporates MB suppression after a prescribed fractional mass loss is introduced by hand and applied uniformly to all three regular metrics. No derivation from the modified surface gravity, horizon structure, or underlying MB mechanism is provided, so the integrated energy release during BBN—and therefore the claimed 10^6–10^8 g window—depends on the specific ansatz rather than on the metrics themselves.
  2. [§4.2] §4.2 and Fig. 3: The relaxation of BBN constraints is shown only for the benchmark k=1. Because the suppression factor is defined in terms of k, the location and width of the new mass window are tied to this choice; no scan over k, no error bands, and no robustness test against shifts in the onset of MB suppression are reported.
  3. [§2.3] §2.3 (Regular metrics): The Hawking temperatures are computed from the regular metrics, yet the subsequent evaporation history reverts to a phenomenological self-similar law rather than integrating the metric-specific grey-body factors or back-reaction. This disconnect means the combined lower temperature plus MB suppression is not a direct prediction of the regular spacetimes.
minor comments (3)
  1. [Abstract] The abstract states the new window is “around 10^6–10^8 g” but the precise boundaries depend on the BBN integration details; a short table or explicit interval in the text would improve clarity.
  2. [§3] Notation for the MB onset mass fraction is introduced without a dedicated symbol or equation number, making it difficult to reproduce the numerical results.
  3. [Figures] Figure captions should explicitly state which curves correspond to Hayward, Bardeen, and Simpson-Visser metrics and whether they include or exclude the MB term.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments. We address each of the major comments below and outline how we plan to revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [§3] §3 (Evaporation model): The self-similar form dM/dt = f(M,k) that incorporates MB suppression after a prescribed fractional mass loss is introduced by hand and applied uniformly to all three regular metrics. No derivation from the modified surface gravity, horizon structure, or underlying MB mechanism is provided, so the integrated energy release during BBN—and therefore the claimed 10^6–10^8 g window—depends on the specific ansatz rather than on the metrics themselves.

    Authors: We agree that the evaporation model is phenomenological and introduced to capture the memory burden suppression effect in a simplified manner. This approach follows the standard treatment in the literature on memory burden effects for black holes. The self-similar form allows for a consistent comparison across the different regular metrics while focusing on the impact of the MB parameter k. A full derivation from first principles would require a detailed model of the MB mechanism in curved spacetime, which is beyond the scope of this work. However, we will revise §3 to explicitly state the phenomenological nature of the model and discuss its motivation from prior studies, making clear that the results depend on this ansatz. revision: partial

  2. Referee: [§4.2] §4.2 and Fig. 3: The relaxation of BBN constraints is shown only for the benchmark k=1. Because the suppression factor is defined in terms of k, the location and width of the new mass window are tied to this choice; no scan over k, no error bands, and no robustness test against shifts in the onset of MB suppression are reported.

    Authors: We chose k=1 as a benchmark value to illustrate the effect. To address this concern, in the revised version we will include additional plots or discussions showing the dependence on k for a range of values (e.g., k=0.5 to 2), and assess the robustness of the 10^6–10^8 g window. This will provide a better understanding of how the mass window varies with the MB strength. revision: yes

  3. Referee: [§2.3] §2.3 (Regular metrics): The Hawking temperatures are computed from the regular metrics, yet the subsequent evaporation history reverts to a phenomenological self-similar law rather than integrating the metric-specific grey-body factors or back-reaction. This disconnect means the combined lower temperature plus MB suppression is not a direct prediction of the regular spacetimes.

    Authors: The Hawking temperatures are calculated directly from the regular metrics to demonstrate the reduction in temperature relative to the Schwarzschild case, which is a key motivation for considering regular PBHs. The evaporation law is then modeled phenomenologically to incorporate the additional MB suppression, which is an independent effect not encoded in the metric itself. This separation allows us to study the synergistic impact of both ingredients. We will add text in §2.3 and §3 to clarify this modeling choice and note that a more integrated calculation including grey-body factors would be a valuable extension for future work. revision: partial

Circularity Check

1 steps flagged

MB strength k=1 benchmark directly produces claimed mass window via phenomenological evaporation ansatz

specific steps
  1. fitted input called prediction [Abstract]
    "Assuming a phenomenological self-similar evaporation, we find that the MB effect significantly relaxes the evaporation constraints. For a benchmark of the MB strength parameter k=1, a new PBH mass window opens at around 10^6--10^8 g, where regular PBHs can compose all dark matter without violating the Big Bang nucleosynthesis bounds."

    The evaporation rate is defined to incorporate MB suppression controlled by the free parameter k; choosing the benchmark value k=1 then directly yields the relaxed BBN constraint and the new mass window. The 'prediction' is therefore the numerical consequence of the modeling assumption rather than an output independent of the chosen functional form.

full rationale

The central claim of a new 10^6-10^8 g PBH dark-matter window for k=1 rests on a self-similar evaporation law dM/dt = f(M,k) that is introduced by assumption and activates suppression after a fixed fractional mass loss. This functional form is not derived from the Hayward/Bardeen/Simpson-Visser surface gravity or grey-body factors; instead the suppression factor is defined in terms of the free parameter k. Setting the benchmark k=1 therefore forces the integrated energy release during BBN to fall below the bound, making the mass window a direct output of the input ansatz rather than an independent derivation. No external benchmark or first-principles calculation is shown to fix k, so the result reduces to the modeling choice.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The result depends on a phenomenological evaporation law and a tunable memory-burden strength parameter whose value is chosen to open the desired window.

free parameters (1)
  • MB strength parameter k
    Benchmarked at k=1 to produce the 10^6-10^8 g window; controls the strength of evaporation suppression after initial mass loss.
axioms (2)
  • domain assumption Regular black hole metrics (Hayward, Bardeen, Simpson-Visser) lower Hawking temperature relative to Schwarzschild.
    Invoked to justify slower baseline evaporation before memory burden is applied.
  • ad hoc to paper Self-similar evaporation remains valid when memory burden is active.
    Phenomenological assumption stated in the abstract that allows analytic treatment of mass loss.

pith-pipeline@v0.9.0 · 5743 in / 1471 out tokens · 28452 ms · 2026-05-20T03:03:55.324735+00:00 · methodology

discussion (0)

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