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arxiv: 2606.25023 · v1 · pith:PAVA3VNYnew · submitted 2026-06-23 · 🌀 gr-qc · hep-th

Obstructions to Minimal Regular Black Hole Cosmologies

Damien A. Easson This is my paper

Pith reviewed 2026-06-25 21:59 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords regular black holesFRW cosmologyDarmois matchingMisner-Sharp massasymptotic flatnessgeodesic completenessANECKantowski-Sachs
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The pith

Static asymptotically flat regular black holes obstruct indefinitely expanding FRW daughter cosmologies.

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

The paper derives that a static regular black hole cannot match onto an FRW cosmology that expands indefinitely without extra ingredients. The trapped region inside such black holes is Kantowski-Sachs rather than FRW, so any cosmological region must be introduced as a separate matched daughter. For closed daughters the angular matching condition forces the induced density to fall as the cube of the scale factor while the curvature term falls only as the square, bounding the expansion. Flat and open daughters are ruled out by a general completeness theorem that applies when the spacetime is curvature-regular and obeys the average null energy condition.

Core claim

The trapped region of a static asymptotically flat regular black hole is Kantowski-Sachs, requiring the FRW daughter to be a separate matched region. Asymptotic flatness together with finite ADM mass implies that the Misner-Sharp mass controls the angular Darmois condition, forcing the density on a closed daughter to decay as A^{-3} while the k=+1 term decays only as A^{-2}; the minimal closed branch is therefore bounded. Flat and open daughters are excluded by the general FRW completeness theorem for non-static curvature-regular ANEC-consistent cases. The Bardeen source supplies no natural late-time support for an unbounded closed daughter.

What carries the argument

Angular Darmois matching condition controlled by the Misner-Sharp mass, which enforces the A^{-3} density decay relative to the A^{-2} curvature term for closed daughters.

If this is right

  • Closed FRW daughters matched to such parents must be bounded rather than indefinitely expanding.
  • Flat and open FRW daughters matched to such parents cannot be geodesically complete.
  • The Bardeen source alone cannot furnish late-time support for an unbounded closed daughter.
  • A viable FRW daughter requires at least one of modified asymptotics, nonminimal matching, non-FRW evolution, or an extra stress-energy component.

Where Pith is reading between the lines

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

  • Relaxing asymptotic flatness or allowing a dynamical parent black hole might evade the density-curvature mismatch.
  • Numerical evolution of the matched geometry could reveal whether singularities or geodesic incompleteness appear exactly where the analytic argument predicts.
  • Similar obstructions may appear in other regular-black-hole-to-cosmology transition models that assume finite-mass static parents.

Load-bearing premise

The parent black hole is static, asymptotically flat with finite ADM mass, the daughter is exactly FRW, and the matching obeys standard Darmois conditions while the geometry remains curvature-regular and satisfies ANEC.

What would settle it

Explicit construction of a geodesically complete non-static curvature-regular ANEC-satisfying FRW spacetime matched via standard Darmois conditions to a static asymptotically flat regular black hole of finite ADM mass.

Figures

Figures reproduced from arXiv: 2606.25023 by Damien A. Easson.

Figure 1
Figure 1. Figure 1: FIG. 1. Closed Bardeen daughter evolution in the asymptotically flat case. The plotted quantity [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
read the original abstract

We derive an obstruction to FRW daughter cosmologies from static, asymptotically flat regular black holes. The trapped region of such a parent is Kantowski--Sachs rather than FRW, so the daughter must be introduced as a separate matched region. For closed daughters, the angular Darmois condition is controlled by the Misner--Sharp mass: asymptotic flatness and finite ADM mass force the induced density to decay as $A^{-3}$, while the $k=+1$ curvature term scales as $A^{-2}$. The minimal closed branch is therefore bounded rather than indefinitely expanding. Flat and open daughters avoid this boundedness mechanism, but the general flat/open FRW completeness theorem prevents non-static curvature-regular, ANEC-consistent flat/open daughters from being geodesically complete. For Bardeen, the parent source does not naturally supply the late-time support needed for an unbounded closed daughter. A viable FRW daughter therefore requires additional structure, such as modified asymptotics, nonminimal matching, non-FRW evolution, or an additional stress-energy component.

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

2 major / 2 minor

Summary. The paper claims that static, asymptotically flat regular black holes cannot support minimal FRW daughter cosmologies. The trapped region is Kantowski-Sachs, requiring separate matching via Darmois conditions. For closed daughters, asymptotic flatness and finite ADM mass imply via the Misner-Sharp mass that the induced density decays as A^{-3} while the k=+1 term scales as A^{-2}, bounding the evolution. Flat and open daughters are excluded by a general FRW completeness theorem for non-static, curvature-regular, ANEC-consistent cases. The Bardeen source is shown not to supply late-time support for unbounded closed daughters, so viable models require additional structure such as modified asymptotics or extra stress-energy.

Significance. If the derivations hold, the result establishes a clear obstruction to minimal regular black hole cosmologies using only standard GR junction conditions, the Misner-Sharp mass, and known completeness theorems. This is a parameter-free no-go result grounded in asymptotic flatness and finite ADM mass, providing useful guidance for model-building in regular black holes and their cosmological extensions. The direct derivation of the A^{-3} scaling and application of the completeness theorem are strengths.

major comments (2)
  1. [Closed daughters analysis] The boundedness claim for closed daughters rests on the angular Darmois condition forcing density ~ A^{-3} from the Misner-Sharp mass approaching a constant at the matching surface (abstract). The manuscript should explicitly display the relevant junction equation or Misner-Sharp expression to confirm the mass remains constant rather than acquiring time dependence from the matching.
  2. [Flat/open daughters analysis] The exclusion of flat/open daughters invokes 'the general flat/open FRW completeness theorem' under ANEC and curvature regularity (abstract). The manuscript must state the precise theorem (including reference) and verify that the matched geometry preserves the hypotheses (ANEC across the surface, curvature regularity of the daughter) without additional assumptions.
minor comments (2)
  1. [Abstract/Introduction] The abstract refers to 'minimal closed branch' and 'daughter' without prior definition; a brief clarification of these terms in the introduction would improve readability.
  2. [Bardeen example] The Bardeen source analysis is summarized in one sentence; expanding the explicit stress-energy mismatch at late times would strengthen the claim that it 'does not naturally supply' the required support.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. The comments identify opportunities to strengthen the presentation by making key equations and references explicit. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Closed daughters analysis] The boundedness claim for closed daughters rests on the angular Darmois condition forcing density ~ A^{-3} from the Misner-Sharp mass approaching a constant at the matching surface (abstract). The manuscript should explicitly display the relevant junction equation or Misner-Sharp expression to confirm the mass remains constant rather than acquiring time dependence from the matching.

    Authors: We agree that an explicit display of the junction condition will improve clarity. In the revised manuscript we will insert the angular Darmois matching equation together with the Misner-Sharp mass expression evaluated at the surface, showing that asymptotic flatness plus finite ADM mass fixes the mass to a constant value independent of the matching time coordinate, thereby confirming the A^{-3} density scaling without additional time dependence. revision: yes

  2. Referee: [Flat/open daughters analysis] The exclusion of flat/open daughters invokes 'the general flat/open FRW completeness theorem' under ANEC and curvature regularity (abstract). The manuscript must state the precise theorem (including reference) and verify that the matched geometry preserves the hypotheses (ANEC across the surface, curvature regularity of the daughter) without additional assumptions.

    Authors: We will cite the precise completeness theorem (including its reference) in the revised text. We will also add a short paragraph verifying that the Darmois matching preserves ANEC (the parent satisfies ANEC by regularity and the junction is C^1) and that the daughter remains curvature-regular by construction of the matching, thereby confirming that the hypotheses of the theorem continue to hold. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation applies standard Darmois junction conditions to a static asymptotically flat parent with finite ADM mass, yielding the A^{-3} density scaling directly from the Misner-Sharp mass approaching a constant (contrasted with the k=+1 term scaling as A^{-2}); this is ordinary closed FRW dynamics. Flat/open cases are excluded by an external general completeness theorem under ANEC and curvature regularity. No self-definitional steps, fitted inputs renamed as predictions, load-bearing self-citations, or ansatz smuggling appear; all load-bearing elements are independent GR results or external theorems, making the chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The central claim rests entirely on standard general relativity assumptions without new free parameters or invented entities.

axioms (3)
  • standard math Einstein field equations hold in both regions
    Invoked for the Misner-Sharp mass and curvature terms throughout the matching analysis.
  • domain assumption Darmois junction conditions apply at the matching surface
    Used to relate the angular component to the Misner-Sharp mass and induced density.
  • domain assumption Averaged null energy condition (ANEC) holds
    Required for the general flat/open FRW completeness theorem cited in the abstract.

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Reference graph

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