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arxiv: 2605.30446 · v1 · pith:3WSCYOFQnew · submitted 2026-05-28 · 🌀 gr-qc

Cosmological accretion onto braneworld black holes: a relativistic treatment

Itzi Aldecoa-Tamayo , Christian T. Byrnes , David Seery This is my paper

Pith reviewed 2026-06-29 05:40 UTC · model grok-4.3

classification 🌀 gr-qc
keywords braneworld black holesprimordial black holesaccretionRandall-Sundrumcosmological evolutionfive-dimensional gravitydark matter
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The pith

Braneworld effects drive far stronger early accretion onto primordial black holes than four-dimensional models allow.

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

The paper re-examines how black holes on a Randall-Sundrum brane pull in cosmological fluid. It combines the Shiromizu-Maeda-Sasaki projection with Michel's relativistic accretion solution to show that five-dimensional corrections extend and intensify the accretion phase at early times. This changes the relation between the mass a black hole starts with and the mass it reaches today, sometimes by several orders of magnitude. A reader would care because the result revises whether light primordial black holes could grow enough to explain dark matter or other observations.

Core claim

Braneworld effects play a significant role in the early Universe, strongly impacting the evolution of light primordial black holes. The mapping between initial conditions and present-day PBH populations is substantially modified by an extended phase of early-time accretion that is significantly more efficient than previously found. For certain regions of parameter space, PBHs that could contribute to the present-day dark matter abundance may have formed with masses below the effective four-dimensional Planck scale. The discrepancy between our black hole masses and the most optimistic previous estimates grows as t^{0.34}, reaching up to ∼10^5 for the smallest M_5 permitted by observations.

What carries the argument

Michel's 1972 relativistic spherical accretion solution projected onto the brane via the Shiromizu-Maeda-Sasaki formalism and Gauss-Codazzi equations, which alters the effective density and velocity of the accreting fluid.

If this is right

  • Light primordial black holes can reach masses large enough to contribute to dark matter even when they form below the four-dimensional Planck scale.
  • The present-day abundance of black holes that formed early is substantially higher than four-dimensional estimates imply.
  • The strongest enhancement occurs for the smallest allowed values of the five-dimensional Planck scale M_5.
  • Accretion remains efficient over a longer interval than in standard cosmology, altering the time at which black holes transition from accretion-dominated to other evolutionary regimes.

Where Pith is reading between the lines

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

  • If the result holds, constraints on primordial black holes as dark matter derived from four-dimensional accretion models would need to be recomputed from scratch.
  • The same formalism could be applied to other early-universe objects whose growth is sensitive to the effective gravitational strength on the brane.
  • Future gravitational-wave or microlensing surveys targeting sub-solar-mass black holes would provide a direct test of the modified growth law.

Load-bearing premise

Michel's 1972 accretion solution together with the braneworld projection equations fully describes the fluid-black hole interaction without further five-dimensional corrections or back-reaction on the brane geometry.

What would settle it

A direct measurement or simulation of primordial black hole masses at the end of the radiation era that fails to show the predicted t^{0.34} growth factor relative to four-dimensional accretion would falsify the central claim.

read the original abstract

Higher-dimensional black holes have been extensively studied over the years, primarily from heuristic and fundamental perspectives or within the context of holographic applications. However, their interaction with ordinary matter confined to the brane is also of particular interest in cosmology. In this work, we revisit accretion within the Randall-Sundrum type II framework, employing the covariant Shiromizu-Maeda-Sasaki formalism together with the Gauss-Codazzi and energy conservation equations. We analyse information propagation in the cosmological fluid and implement a fully relativistic treatment of accretion following Michel's prescription. We find that braneworld effects play a significant role in the early Universe, strongly impacting the evolution of light primordial black holes (PBHs). In particular, the mapping between initial conditions and present-day PBH populations is substantially modified by an extended phase of early-time accretion that is significantly more efficient than previously found. For certain regions of parameter space, PBHs that could contribute to the present-day dark matter abundance may have formed with masses below the effective four-dimensional Planck scale. The discrepancy between our black hole masses and the most optimistic previous estimates grows as $t^{0.34}$-a significant difference that reaches up to several orders of magnitude by the end of the strong-accretion epoch, particularly for black holes that form early and for small values of the fundamental Planck scale $M_5$, reaching up to $\sim 10^5$ for the smallest $M_5$ permitted by observations.

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

1 major / 0 minor

Summary. The paper claims that within the Randall-Sundrum II braneworld, the Shiromizu-Maeda-Sasaki (SMS) formalism combined with Gauss-Codazzi equations and Michel's 1972 relativistic steady-state accretion solution yields substantially more efficient early-universe accretion onto primordial black holes than prior estimates. This produces a mass discrepancy that grows as t^{0.34}, reaching factors up to ~10^5 by the end of the strong-accretion epoch for early-forming PBHs and small M_5, implying that PBHs contributing to present-day dark matter could have formed with initial masses below the effective 4D Planck scale.

Significance. If the central result holds, the work would meaningfully revise the mapping between PBH formation conditions and present-day abundances, expanding the viable parameter space for PBH dark matter and highlighting the importance of braneworld corrections during radiation domination. The explicit use of a covariant 4D effective treatment and relativistic accretion is a methodological strength.

major comments (1)
  1. [Abstract (method paragraph)] Abstract (method paragraph): the central t^{0.34} scaling and the factor-of-10^5 discrepancy are obtained by integrating the Michel accretion rate into the SMS-projected continuity and Einstein equations. The manuscript must explicitly demonstrate that bulk Weyl-tensor contributions beyond the standard dark-radiation term, as well as any back-reaction of the radial inflow on the brane geometry, remain negligible throughout the radiation era when the horizon size approaches the AdS radius set by M_5; otherwise the effective sound speed and capture cross-section used in the integration are not justified.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The single major comment identifies a necessary justification for the validity of the effective 4D treatment in the regime where the horizon size approaches the AdS radius. We address this point directly below and will revise the manuscript to incorporate the requested demonstration.

read point-by-point responses

  1. Referee: [Abstract (method paragraph)] Abstract (method paragraph): the central t^{0.34} scaling and the factor-of-10^5 discrepancy are obtained by integrating the Michel accretion rate into the SMS-projected continuity and Einstein equations. The manuscript must explicitly demonstrate that bulk Weyl-tensor contributions beyond the standard dark-radiation term, as well as any back-reaction of the radial inflow on the brane geometry, remain negligible throughout the radiation era when the horizon size approaches the AdS radius set by M_5; otherwise the effective sound speed and capture cross-section used in the integration are not justified.

    Authors: We agree that an explicit demonstration of the negligibility of higher-order bulk Weyl contributions and back-reaction is required for the regime in which the black-hole horizon becomes comparable to the AdS radius. The SMS projection already encodes the leading dark-radiation term (the projected Weyl tensor component that behaves as radiation), but the manuscript does not currently quantify the size of the remaining bulk terms or the perturbation to the brane geometry induced by the radial inflow. In the revised version we will add a dedicated subsection (and supporting estimates in an appendix) that compares the magnitude of the neglected Weyl components to the dark-radiation term using the Gauss-Codazzi relations and the characteristic scales of the radiation-dominated era. We will also estimate the back-reaction by comparing the accretion-induced stress-energy perturbation to the background brane tension and curvature scale set by M_5. These estimates will be performed for the parameter ranges (early formation times and smallest observationally allowed M_5) that produce the reported t^{0.34} growth and 10^5 mass discrepancy, thereby confirming that the Michel solution and the adopted sound speed remain applicable. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies external 1972 Michel solution and SMS formalism to obtain t^{0.34} growth

full rationale

The paper computes the reported mass discrepancy (growing as t^{0.34}, up to 10^5) by inserting Michel's 1972 relativistic accretion solution into the Shiromizu-Maeda-Sasaki projected Einstein equations and Gauss-Codazzi relations on the brane, then integrating the resulting continuity equation for the cosmological fluid. No equation or result is defined in terms of itself, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests on a self-citation whose content is unverified. The t^{0.34} scaling is an output of the integration under the stated assumptions rather than an input by construction, and the cited formalisms (Michel 1972, SMS 2000) are independent of the present authors.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Abstract-only review prevents exhaustive ledger; the central claim rests on the validity of the SMS formalism and Michel accretion solution applied to RSII, plus the assumption that the five-dimensional Planck scale M_5 is an external input.

free parameters (1)
  • M_5
    Fundamental five-dimensional Planck scale treated as a free parameter bounded by observations; the reported discrepancy reaches 10^5 for its smallest allowed value.
axioms (2)
  • domain assumption Shiromizu-Maeda-Sasaki formalism plus Gauss-Codazzi equations correctly describe the effective four-dimensional dynamics of braneworld black holes.
    Invoked in the method paragraph of the abstract as the framework for the entire calculation.
  • domain assumption Michel's 1972 relativistic accretion solution remains valid when transplanted to the braneworld geometry.
    Explicitly stated as the prescription followed for the accretion treatment.

pith-pipeline@v0.9.1-grok · 5799 in / 1553 out tokens · 25523 ms · 2026-06-29T05:40:40.529035+00:00 · methodology

discussion (0)

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Reference graph

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