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No-shell FRW daughters matched to asymptotically flat regular black holes are bounded if closed and past-incomplete if flat or open; a regular core alone cannot yield a viable daughter cosmology.

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2026-08-04 01:47 UTC pith:PAVA3VNY

arxiv 2606.25023 v3 pith:PAVA3VNY submitted 2026-06-23 gr-qc hep-th

Obstructions to Minimal Regular Black Hole Cosmologies

Damien A. Easson This is my paper
classification gr-qc hep-th
keywords daughterflrwclosedadditionalblackcosmologiescurvaturedaughters
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Some physicists have wondered whether the inside of a black hole could be a kind of baby universe. In ordinary Schwarzschild geometry the trapped interior can be rewritten as a Kantowski–Sachs spacetime — a squashed, non-uniform space — not as a smooth homogeneous and isotropic cosmology. The paper therefore studies the next simplest idea: cut the parent black hole at a spherical surface and glue on a separate Friedmann–Lemaître–Robertson–Walker (FRW) patch without a shell of matter.

The gluing imposes a Friedmann equation on the daughter, controlled by the parent's Misner–Sharp mass: H² + k/A² = 2m(R_b)/R_b³, where R_b is the boundary radius. For a closed (spherical) daughter, k = +1. Asymptotic flatness and finite ADM mass make the mass term behave like dust, falling as A⁻³, while the curvature term falls as A⁻² and dominates at large scale factor. So the closed daughter is bounded: it expands from a bounce, turns around, and recollapses. Adding a redshift function to the parent does not rescue it. Flat and open daughters avoid the turnaround, but the paper applies a completeness theorem (from the author's companion papers) stating that non-static, curvature-regular flat/open FRW spacetimes with regular affine ends cannot be simultaneously null geodesically complete and ANEC-consistent. The Bardeen example is explicitly past-incomplete because its de Sitter-like beginning has finite past affine length. The paper also argues the Bardeen matter cannot supply late-time support.

The conclusion is a list of escape routes: shells, modified asymptotics, non-FRW daughters, or extra stress-energy. The paper does not claim a general no-go for all black-hole-universe constructions.

Core claim

Theorem 1 (Sec. V): 'Consider a static, spherically symmetric, asymptotically flat parent spacetime in the one-function class g_tt g_rr = −1, with finite ADM mass M > 0. Attach an FRW daughter across a nondegenerate comoving spherical Darmois boundary. Assume that the matching is no-shell... Then the closed daughter branch is bounded at finite scale factor... For flat and open daughters... a non-static curvature-regular FRW spacetime with k = 0 or k = −1 and regular affine ends cannot be both null geodesically complete and ANEC-consistent.' If correct, no minimal no-shell FRW daughter of an asymptotically flat regular black hole is simultaneously indefinitely expanding, curvature-regular, geodesically complete, and ANEC-consistent; the closed-branch part is the new content, enforced by m(R) → M through H² = −1/A² + 2M/(A³ sin³ψ_b) + o(A⁻³) (Eq. 55).

Load-bearing premise

The flat/open leg of Theorem 1 is carried by the 'flat/open FRW completeness theorem' of the author's companion papers [3,4], stated in Sec. V but not proven here, under the 'regular affine ends' caveat of footnote 3; if that theorem is false or inapplicable, the flat/open half collapses even though the closed-branch result (Sec. V.A, Prop. 2) stands on its own derivation. A second structural premise: completeness is assessed for the maximal FRW continuation of A(τ) rather than for the actual parent+daughter matched spacetime (Sec. V.C), leaving open whether radial null geodesics might leave the daughter through the junction before their affine parameter ends. The declared scope restriction g_tt g_rr = −1 (Sec. I) is also load-bearing for the flat/open dichotomy; only the closed branch is extended to redshifted parents (Sec. IVB).

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

No numbers are fitted to data; the inputs are the parent metric parameters (Bardeen M, g), declared junction data (ψ_b or χ_b), and the theorem hypotheses. The genuinely adjustable choices — junction location and the tuning limits of Sec. V.B — are explicitly labeled by the authors as junction data and tuning, not predictions. The analysis rests on the one-function static class restriction, the imposed ANEC criterion, standard no-shell Darmois matching, and, for the flat/open leg, the author's companion completeness theorem [3,4].

axioms (5)
  • domain assumption Flat/open FRW completeness theorem: a non-static curvature-regular FRW spacetime with k=0 or k=−1 and regular affine ends cannot be both null geodesically complete and ANEC-consistent (refs [3,4]).
    Invoked without proof in Sec. V (and footnote 3) to obstruct flat/open daughters; both supporting references are co-authored by the present author and are not available for independent verification here.
  • domain assumption ANEC along complete null geodesics is imposed as the minimal non-exoticity criterion.
    Sec. I; dropping ANEC removes the flat/open obstruction, and the imported completeness theorem is formulated under the same assumption.
  • domain assumption Main dichotomies are restricted to the one-function static spherical class g_tt g_rr = −1.
    Sec. I; only the closed-branch boundedness is extended to redshifted parents (Sec. IVB), so the flat/open claim is unproven outside this class.
  • domain assumption Standard Darmois–Israel no-shell matching with a comoving boundary at fixed χ_b (or ψ_b); daughter evolution is fixed entirely by the parent metric profile.
    Sec. IV.A and Appendix A; this defines 'minimal daughter'; shells or non-comoving boundaries are the escape routes listed in Sec. V.D.
  • domain assumption Asymptotic flatness with F(R) = 1 − 2M/R + o(R⁻¹) and finite ADM mass M > 0.
    Hypothesis of Theorem 1 and Prop. 2; the entire closed-branch argument turns on m(R) → M.

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Pith. "Pith review of Obstructions to Minimal Regular Black Hole Cosmologies." pith.science (2026). https://pith.science/paper/PAVA3VNY

@misc{pith2026260625023,
  author       = {Pith},
  title        = {Pith review of: Obstructions to Minimal Regular Black Hole Cosmologies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PAVA3VNY}},
  note         = {Machine review of arXiv:2606.25023}
}
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read the original abstract

We derive an obstruction to Friedmann--Lema\^itre--Robertson--Walker (FLRW) daughter cosmologies from static, asymptotically flat regular black holes. The trapped region of such a parent is Kantowski--Sachs rather than FLRW, 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. For their maximal homogeneous FLRW continuations, the regular-end affine-ANEC theorem excludes simultaneous non-staticity, curvature regularity, null geodesic completeness, and ANEC consistency. For Bardeen, the parent source does not naturally supply the late-time support needed for an unbounded closed daughter. Within these criteria, a viable FLRW daughter therefore requires additional structure, such as modified asymptotics, nonminimal matching, non-FLRW evolution, or an additional stress-energy component.

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 ↗

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