arxiv: 2605.00252 · v1 · submitted 2026-04-30 · ✦ hep-ph · gr-qc· hep-ex· hep-th

Recognition: unknown

Micron-sized Extra Dimensions and Primordial Black Holes: Charges, Rotating, and Memory Burdened

George K. Leontaris, George Prampromis

Authors on Pith no claims yet

Pith reviewed 2026-05-09 19:30 UTC · model grok-4.3

classification ✦ hep-ph gr-qchep-exhep-th

keywords primordial black holesextra dimensionsdark mattermemory burdenKaluza-Klein modesHawking evaporationneutrino mass scale

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The pith

Six-dimensional primordial black holes can survive as light dark matter when memory burden suppresses their evaporation, with a fundamental scale near 10 TeV.

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

The paper investigates whether primordial black holes in a six-dimensional spacetime with two extra dimensions can account for dark matter. It considers charged and rotating black holes under both standard Hawking radiation and the memory burden effect that slows evaporation. Under standard evaporation only heavier black holes persist, but memory burden allows much lighter ones to remain today. These micro black holes could produce detectable high-multiplicity events at future particle colliders, and their Kaluza-Klein mass splitting matches the scale of atmospheric neutrinos, pointing to possible connections across different physical regimes.

Core claim

In six dimensions with two extra dimensions, the memory burden mechanism suppresses evaporation of primordial black holes so that sub-gram mass objects can survive to the present and serve as dark matter candidates, while near-extremal charged or rotating configurations have extended lifetimes, and the Kaluza-Klein splitting Δm aligns with the atmospheric neutrino mass difference.

What carries the argument

The memory burden scenario, which enormously suppresses the evaporation rate of black holes beyond standard Hawking radiation.

Load-bearing premise

That the memory burden effect applies to suppress evaporation for these six-dimensional charged and rotating black holes without a detailed first-principles derivation.

What would settle it

Observation or absence of high-multiplicity micro black hole events at the Future Circular Collider with the predicted multiplicity and thermal spectrum would confirm or rule out the scenario for the proposed mass range.

read the original abstract

We explore the possibility of explaining dark matter through six-dimensional (6D) primordial black holes (PBHs) in a theory with two extra dimensions. Interestingly, in this scenario the fundamental energy scale is of the order of $\sim 10$ TeV, accessible by future experiments. We analyse the viability of charged and rotating 6D black holes under standard Hawking evaporation as well as the memory burden scenario. In the case of pure Hawking evaporation, only PBHs with masses $M > 10^8$ g survive to present, while the lifetime of near-extremal configurations is extended by a factor $1/\beta^{1/2}$, where the parameter $\beta$ characterizes small deviations from extremality. In the memory burden scenario evaporation is enormously suppressed, and sub-gram mass PBHs can survive to the present epoch. At future colliders such as the Future Circular Collider, these micro black holes produce characteristic high multiplicity events, $\langle N \rangle \sim 21$, with thermal spectra, enabling direct probes of the fundamental scale and the number of extra dimensions. We find that the memory burden mechanism opens a broad new mass window for light PBH dark matter, while the Kaluza-Klein mass splitting $\Delta m$ aligns with the atmospheric neutrino scale, suggesting a unified framework between Swampland constraints, cosmology, collider physics, and low energy phenomenology.

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.

Desk Editor's Note private letter to a colleague

Applies memory burden to 6D charged/rotating PBHs but the suppression and neutrino-scale link rest on assumptions rather than derivations.

read the letter

This paper takes the memory burden scenario for slowing black hole evaporation and applies it to six-dimensional primordial black holes that carry charge and rotation, with a fundamental scale near 10 TeV. The central claim is that this suppression lets sub-gram PBHs survive as dark matter while the Kaluza-Klein splitting lines up with the atmospheric neutrino mass difference, tying together extra dimensions, cosmology, and low-energy physics. Under ordinary Hawking radiation the paper finds only masses above 10^8 g persist, with near-extremal cases gaining a lifetime factor of 1/sqrt(beta), but memory burden then opens a much wider light-mass window. It also sketches collider signals at the FCC with average multiplicity around 21 and thermal spectra. The work is clear in laying out these viability checks and in connecting the dots to existing PBH and extra-dimension literature. It treats the charged and rotating cases explicitly rather than defaulting to Schwarzschild, which is a small but useful step. The soft spots are straightforward. The memory-burden suppression is invoked as enormous without a derivation showing how the back-reaction or information-storage mechanism works for the 6D metric, charge, or angular momentum; the factor is taken from the four-dimensional literature and assumed to carry over. The Delta-m alignment with the neutrino scale is presented as suggestive rather than fixed by the compactification radius or moduli stabilization, so it functions more as a post-hoc observation than a model output. No explicit lifetime integrals, error estimates, or regime-validation checks appear in the sections I could access, which leaves the quantitative mass window sensitive to the size of the suppression. The paper is aimed at people already working on PBH dark matter in extra dimensions or on memory-burden effects. A reader in those subfields will get a concrete parameter-space sketch and collider phenomenology to think about, even if the new results are mostly extensions rather than first-principles derivations. It shows honest engagement with the relevant papers and does not hide the assumptions, so it counts as serious thinking on its own terms. I would send it to peer review. Referees can ask for the missing derivations on the 6D memory-burden regime and for a clearer statement of what is calculated versus assumed; the ideas are worth checking even if the current version needs tightening.

Referee Report

2 major / 2 minor

Summary. The paper explores six-dimensional primordial black holes (PBHs) with two extra dimensions as dark matter candidates, with a fundamental scale of order 10 TeV. It analyzes the viability of charged and rotating 6D black holes under standard Hawking evaporation, finding that only masses above 10^8 g survive while near-extremal lifetimes are extended by a factor 1/sqrt(beta), and under the memory burden scenario, where evaporation is enormously suppressed allowing sub-gram PBHs to survive to the present. The work also discusses collider signatures at facilities like the Future Circular Collider, with average multiplicity around 21 and thermal spectra, and notes that the Kaluza-Klein mass splitting Delta m aligns with the atmospheric neutrino scale, suggesting a unified framework connecting Swampland constraints, cosmology, collider physics, and low-energy phenomenology.

Significance. If the memory burden suppression is rigorously derived and applicable to 6D charged/rotating cases, the result would substantially broaden the viable mass window for light PBH dark matter and offer concrete collider predictions (e.g., high-multiplicity events with <N> ~ 21) that could probe the fundamental scale and extra dimensions. The suggested alignment with neutrino scales provides an intriguing potential link across scales, though this remains suggestive. The analysis of lifetime extensions under both evaporation regimes is a clear strength.

major comments (2)

[Viability analysis under memory burden scenario] The central claim that the memory burden scenario opens a broad new mass window for sub-gram PBH dark matter rests on the assertion that evaporation is 'enormously suppressed' for 6D near-extremal charged and rotating black holes. However, no explicit derivation is provided for how the memory-burden back-reaction or information-storage mechanism applies to the higher-dimensional metric, charge, or angular momentum (see the viability analysis under the memory burden scenario). This is load-bearing, as the quantitative survival of sub-gram masses depends directly on the suppression factor.
[Discussion of Kaluza-Klein mass splitting and unified framework] The alignment of the Kaluza-Klein mass splitting Delta m with the atmospheric neutrino scale is presented as suggestive of a unified framework, but without a first-principles derivation fixing the compactification radius or moduli stabilization to this value (see the discussion linking to low-energy phenomenology). While not the primary claim, it underpins the broader unification narrative.

minor comments (2)

[Pure Hawking evaporation analysis] The parameter beta characterizing deviations from extremality is introduced in the lifetime extension factor 1/beta^{1/2}, but its allowed range and physical motivation in the 6D context could be clarified with additional bounds or examples.
[Collider signatures] The collider signature estimate of average multiplicity <N> ~ 21 is a useful concrete prediction, but it would benefit from a brief explanation of how this number is obtained from the 6D black hole parameters.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the positive assessment of our work and for the detailed comments that have helped us improve the manuscript. Below we provide point-by-point responses to the major comments.

read point-by-point responses

Referee: [Viability analysis under memory burden scenario] The central claim that the memory burden scenario opens a broad new mass window for sub-gram PBH dark matter rests on the assertion that evaporation is 'enormously suppressed' for 6D near-extremal charged and rotating black holes. However, no explicit derivation is provided for how the memory-burden back-reaction or information-storage mechanism applies to the higher-dimensional metric, charge, or angular momentum (see the viability analysis under the memory burden scenario). This is load-bearing, as the quantitative survival of sub-gram masses depends directly on the suppression factor.

Authors: We thank the referee for this important observation. The memory burden scenario relies on the back-reaction from the information content of the black hole, which suppresses the Hawking radiation rate once a fraction of the mass has evaporated. This mechanism is expected to apply in higher dimensions because the thermodynamic relations, including entropy proportional to the horizon area, hold in 6D. For charged and rotating black holes, the near-extremal limit reduces the temperature, and the memory burden compounds the suppression. We acknowledge that an explicit adaptation of the 4D derivation to the 6D metric was not included originally. We have therefore added a brief derivation in the revised version, generalizing the information storage argument to the higher-dimensional case and confirming that the suppression factor remains sufficient for sub-gram PBHs to survive. This revision strengthens the viability analysis. revision: partial
Referee: [Discussion of Kaluza-Klein mass splitting and unified framework] The alignment of the Kaluza-Klein mass splitting Delta m with the atmospheric neutrino scale is presented as suggestive of a unified framework, but without a first-principles derivation fixing the compactification radius or moduli stabilization to this value (see the discussion linking to low-energy phenomenology). While not the primary claim, it underpins the broader unification narrative.

Authors: We concur that the connection to the atmospheric neutrino scale is presented as suggestive. The compactification scale is fixed by the TeV fundamental scale in the model, resulting in a Kaluza-Klein splitting that numerically matches the neutrino mass scale. We do not provide a derivation from moduli stabilization or other first principles, as that lies beyond the scope of this work. In the revised manuscript, we have modified the relevant discussion to emphasize the suggestive nature of this alignment and its potential to link different areas of physics, while avoiding any implication of a derived unified framework. This ensures the claims are appropriately qualified. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; claims rest on external scenarios and suggestive alignments rather than self-referential derivations.

full rationale

The paper applies the memory-burden scenario (an external mechanism) to 6D charged/rotating PBHs and states that evaporation is enormously suppressed, opening a sub-gram mass window. It separately notes that the Kaluza-Klein splitting Δm aligns with the atmospheric neutrino scale as a suggestion for unification. These are presented as findings from viability analysis under stated assumptions, not as quantities derived from the paper's own equations that reduce back to inputs by construction. No self-definitional loops, fitted parameters renamed as predictions, or load-bearing self-citations appear in the text. The derivation chain for Hawking lifetimes and collider signatures remains independent of the target claims.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Central claims rest on the memory burden scenario as an external assumption, standard 6D black hole evaporation formulas, and the specific choice of two extra dimensions with ~10 TeV scale; no new entities are invented but the alignment with neutrino scale functions as an ad-hoc observation.

free parameters (2)

beta
Parameter characterizing small deviations from extremality that extends lifetime by 1/sqrt(beta); fitted or chosen to model near-extremal cases.
fundamental scale ~10 TeV
Chosen to make extra dimensions micron-sized and accessible at future colliders.

axioms (2)

domain assumption Standard Hawking evaporation applies to 6D charged and rotating black holes
Invoked for lifetime calculations of M > 10^8 g PBHs.
ad hoc to paper Memory burden scenario enormously suppresses evaporation
Used to allow sub-gram PBHs to survive; treated as given scenario without derivation in abstract.

pith-pipeline@v0.9.0 · 5558 in / 1505 out tokens · 51014 ms · 2026-05-09T19:30:43.640486+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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