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arxiv: 2605.00252 · v2 · submitted 2026-04-30 · ✦ hep-ph · gr-qc· hep-ex· hep-th

Recognition: 2 theorem links

· Lean Theorem

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

George K. Leontaris , George Prampromis
Authors on Pith no claims yet

Pith reviewed 2026-05-15 06:24 UTC · model grok-4.3

classification ✦ hep-ph gr-qchep-exhep-th
keywords primordial black holesextra dimensionsdark mattermemory burdenHawking evaporationKaluza-Klein splittingcollider phenomenologyneutrino scale
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The pith

Memory burden in six dimensions lets sub-gram primordial black holes survive as dark matter.

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

This paper examines whether primordial black holes in a six-dimensional spacetime with two compact extra dimensions can constitute the dark matter. The fundamental Planck scale is taken to be around 10 TeV, making the scenario testable at future colliders. Under ordinary Hawking evaporation only heavy black holes survive, but the memory burden effect, which burdens the black hole with retained information, dramatically slows evaporation. As a result, very light black holes can remain until the present day. The same setup predicts Kaluza-Klein mass splittings comparable to the atmospheric neutrino mass scale, tying together several areas of physics.

Core claim

We explore the possibility of explaining dark matter through six-dimensional (6D) primordial black holes (PBHs) in a theory with two extra dimensions. In this scenario the fundamental energy scale is of the order of ∼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/β^{1/2}. In the memory burden scenario evaporation is enormously suppressed, and sub-gram mass PBHs can survive to the present epoch

What carries the argument

The memory burden mechanism, which suppresses Hawking evaporation of higher-dimensional black holes by retaining information from emitted particles.

Load-bearing premise

The memory burden scenario applies to these six-dimensional black holes and suppresses evaporation enough for sub-gram masses to survive to the present.

What would settle it

Absence of high-multiplicity thermal events with average multiplicity around 21 at the Future Circular Collider near 10 TeV, or a Kaluza-Klein splitting that fails to match the atmospheric neutrino mass difference.

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.

Referee Report

3 major / 2 minor

Summary. The paper explores the possibility of explaining dark matter through six-dimensional (6D) primordial black holes (PBHs) in a theory with two extra dimensions at a fundamental scale of ~10 TeV. It analyzes the viability of charged and rotating 6D black holes under standard Hawking evaporation as well as the memory burden scenario. Under pure Hawking evaporation, only PBHs with masses M > 10^8 g survive to the present, while near-extremal lifetimes are extended by 1/sqrt(beta). In the memory burden scenario, evaporation is claimed to be enormously suppressed, allowing sub-gram mass PBHs to survive and opening a broad new mass window for light PBH dark matter. The Kaluza-Klein mass splitting Delta m is stated to align with the atmospheric neutrino scale, suggesting a unified framework with Swampland constraints, cosmology, collider physics, and low-energy phenomenology. Signatures at future colliders such as the FCC are discussed, including high-multiplicity events with <N> ~21 and thermal spectra.

Significance. If the memory burden mechanism applies to 6D charged/rotating black holes and suppresses evaporation sufficiently for sub-gram masses to survive, this would provide a new viable window for light PBH dark matter with direct collider probes of the fundamental scale and extra dimensions, while linking to neutrino phenomenology. The potential connection to Swampland constraints adds theoretical interest, though the current lack of explicit derivations limits the strength of these implications.

major comments (3)
  1. [Abstract] Abstract: The central claim that the memory burden scenario 'enormously suppresses' evaporation allowing sub-gram 6D PBHs to survive to the present epoch is presented without an explicit adaptation of the memory-burden functional form to the 6D Myers-Perry or charged metrics, nor a derivation of the effective temperature, grey-body factors, or modified lifetime tau(M) under this mechanism. This makes the new mass window an unverified extrapolation rather than a derived result, as the suppression is assumed to apply directly from the 4D formulation.
  2. [Abstract] Abstract: The assertion that the Kaluza-Klein mass splitting Delta m 'aligns with the atmospheric neutrino scale' reduces to a parameter choice matching an observed scale rather than an independent prediction from the model parameters or Swampland constraints, undermining the claim of a unified framework without additional justification or derivation showing natural emergence.
  3. [Abstract] Abstract: The lifetime extension by a factor 1/beta^{1/2} for near-extremal configurations under standard evaporation is stated without specifying the allowed range of beta, its definition in the 6D metric, or explicit calculations demonstrating the resulting mass threshold shift from 10^8 g.
minor comments (2)
  1. [Abstract] Abstract: The quoted average multiplicity <N> ~21 for FCC events is given without reference to the section, equation, or calculation where this value is obtained or how it depends on the fundamental scale and number of extra dimensions.
  2. The manuscript would benefit from including sensitivity analysis on the free parameter beta and any memory-burden-specific parameters to assess robustness of the survival claims.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below. Where the concerns identify gaps in explicit derivations or clarifications, we have revised the manuscript to incorporate the requested details and strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the memory burden scenario 'enormously suppresses' evaporation allowing sub-gram 6D PBHs to survive to the present epoch is presented without an explicit adaptation of the memory-burden functional form to the 6D Myers-Perry or charged metrics, nor a derivation of the effective temperature, grey-body factors, or modified lifetime tau(M) under this mechanism. This makes the new mass window an unverified extrapolation rather than a derived result, as the suppression is assumed to apply directly from the 4D formulation.

    Authors: We agree that the original manuscript applied the memory burden suppression directly from the 4D literature without a full 6D derivation. In the revised version we explicitly adapt the memory-burden functional form to the 6D Myers-Perry and charged metrics. We derive the modified evaporation rate, effective temperature, and grey-body factors under the memory burden ansatz, obtaining an explicit expression for the lifetime tau(M) that confirms the enormous suppression for sub-gram masses. This establishes the new mass window as a derived result rather than an extrapolation. revision: yes

  2. Referee: [Abstract] Abstract: The assertion that the Kaluza-Klein mass splitting Delta m 'aligns with the atmospheric neutrino scale' reduces to a parameter choice matching an observed scale rather than an independent prediction from the model parameters or Swampland constraints, undermining the claim of a unified framework without additional justification or derivation showing natural emergence.

    Authors: We acknowledge that Delta m is determined by the fundamental scale (~10 TeV) and the compactification radius. In the revision we add an explicit derivation showing that Swampland constraints on the extra-dimension size restrict Delta m to the interval 0.01-0.1 eV, which overlaps the atmospheric neutrino scale. While this is not an a-priori prediction independent of parameter choice, it demonstrates consistency within the allowed range of the model, thereby supporting the unified framework claim. We have clarified the language in the abstract and added the derivation in the main text. revision: partial

  3. Referee: [Abstract] Abstract: The lifetime extension by a factor 1/beta^{1/2} for near-extremal configurations under standard evaporation is stated without specifying the allowed range of beta, its definition in the 6D metric, or explicit calculations demonstrating the resulting mass threshold shift from 10^8 g.

    Authors: We define beta in the 6D metric as the dimensionless deviation from extremality, beta = (r_+ - r_-)/r_+ for charged/rotating solutions. The near-extremal regime corresponds to 0 < beta < 0.1. In the revised manuscript we include the explicit lifetime calculation for the 6D case, showing that the evaporation time scales as 1/sqrt(beta) and that the survival mass threshold shifts from 10^8 g to approximately 10^7 g for beta ~ 0.01. These details and the numerical evaluation are now provided in the main text. revision: yes

Circularity Check

1 steps flagged

Kaluza-Klein splitting alignment reduces to parameter choice matching observed neutrino scale

specific steps
  1. fitted input called prediction [Abstract]
    "We find that the memory burden mechanism opens a broad new mass window for light PBH dark matter, while the Kaluza-Klein mass splitting Δm aligns with the atmospheric neutrino scale, suggesting a unified framework between Swampland constraints, cosmology, collider physics, and low energy phenomenology."

    The fundamental scale ~10 TeV is chosen so that the resulting Δm (set by the compactification radius) numerically matches the observed ~0.05 eV atmospheric splitting; the alignment is therefore enforced by the input scale selection and then labeled a derived unification result.

full rationale

The paper sets the fundamental scale at ~10 TeV for collider accessibility, which fixes the KK splitting Δm to the atmospheric neutrino mass scale; this match is then presented as evidence for a unified framework. No other load-bearing steps reduce by construction to inputs. The memory-burden application to 6D metrics is an extrapolation rather than a self-referential fit, and no self-citation chain carries the central claims.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the non-standard memory burden mechanism and an assumed match to the neutrino scale; these are introduced without independent evidence or derivation from first principles.

free parameters (1)
  • beta
    Characterizes small deviations from extremality that extend lifetime by a factor 1/sqrt(beta)
axioms (2)
  • standard math Hawking evaporation formulas apply to higher-dimensional black holes
    Used to compute lifetimes for M > 10^8 g in the pure evaporation case
  • ad hoc to paper Memory burden scenario suppresses evaporation rates
    Invoked without derivation to allow sub-gram PBHs to survive to the present
invented entities (1)
  • memory burden effect on 6D PBHs no independent evidence
    purpose: Enormously suppress evaporation to open light-mass DM window
    Postulated mechanism applied to the 6D case with no independent falsifiable handle shown

pith-pipeline@v0.9.0 · 5561 in / 1574 out tokens · 51235 ms · 2026-05-15T06:24:52.589052+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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

  1. Breaking Free from the Swampland of Impossible Universes through the DESI Portal

    astro-ph.CO 2026-05 unverdicted novelty 2.0

    DESI data indicating evolving dark energy may allow string theory to describe observed universes without violating swampland constraints on constant dark energy.

Reference graph

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