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arxiv: 2606.25755 · v1 · pith:TDWCI2STnew · submitted 2026-06-24 · 🧮 math.DG · gr-qc

C⁰-inextendibility of a class of warped-product black hole spacetimes

Karim Mosani This is my paper

Pith reviewed 2026-06-25 20:45 UTC · model grok-4.3

classification 🧮 math.DG gr-qc
keywords C0-inextendibilitywarped-product spacetimesblack hole singularitiesRiemannian fibreKretschmann scalarglobal hyperbolicity
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The pith

A broad class of warped-product black hole spacetimes are future C^0-inextendible when their fibres are closed, connected, homogeneous and orientable.

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

The paper adapts an existing proof to establish that warped-product black hole spacetimes with a codimension-two fibre cannot be extended continuously into the future past their central singularities. The result applies to nonvacuum models and to geometries that lack spherical symmetry, provided the fibre meets the listed topological and symmetry conditions and the Kretschmann scalar diverges as the radial coordinate approaches zero. A reader would care because the claim shows that the singularities remain genuine barriers to continuous metric extensions in this enlarged family of spacetimes.

Core claim

Under the assumptions that the fibre is closed, connected, homogeneous and orientable, and that the spacetime admits a singularity at r approaching zero marked by diverging Kretschmann scalar, the spacetimes are future C^0-inextendible; the same conclusion holds for models containing more than one regular black hole horizon.

What carries the argument

Adaptation of Sbierski's proof technique to warped-product spacetimes whose metric is built from a static exterior region, a radial warping function r, and a codimension-two Riemannian fibre.

If this is right

  • The inextendibility result applies directly to nonvacuum black hole models.
  • The result covers black hole geometries that lack spherical symmetry.
  • The same conclusion holds for spacetimes that contain more than one regular black hole horizon.

Where Pith is reading between the lines

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

  • The homogeneity assumption on the fibre appears essential for blocking continuous extensions; relaxing it might allow extensions in some cases.
  • The same proof strategy could be tested on warped-product models whose fibres are not compact but still satisfy weaker symmetry conditions.
  • Numerical constructions of interior extensions for these metrics would need to violate at least one of the fibre assumptions to succeed.

Load-bearing premise

The fibre must be closed, connected, homogeneous and orientable, and the Kretschmann scalar must diverge as r approaches zero.

What would settle it

An explicit C^0 extension of the metric across the central region for one such spacetime that still obeys the fibre conditions would falsify the claim.

read the original abstract

We adapt Sbierski's proof of $C^0$-inextendibility of the maximal analytic Schwarzschild spacetime to a broad class of warped-product black hole spacetimes with a static exterior region. These spacetimes are globally hyperbolic, have a codimension-two Riemannian fibre and a radial coordinate $(r)$, which serves as the warping function of the fibre. They admit a spacetime singularity as $r \to 0$, characterised by the divergence of the Kretschmann scalar. This class encompasses nonvacuum black hole models and geometries beyond spherical symmetry. Under suitable assumptions, including that the fibre is closed (compact without boundary), connected, homogeneous, and orientable, we establish future $C^0$-inextendibility for spacetimes in this class. The result further extends to spacetimes possessing more than one regular black hole horizon.

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

0 major / 1 minor

Summary. The manuscript adapts Sbierski's proof of C^0-inextendibility of the maximal analytic Schwarzschild spacetime to a broad class of warped-product black hole spacetimes with a static exterior region. These spacetimes are globally hyperbolic, have a codimension-two Riemannian fibre and a radial coordinate (r) serving as the warping function of the fibre. They admit a spacetime singularity as r → 0 characterised by the divergence of the Kretschmann scalar. Under suitable assumptions, including that the fibre is closed (compact without boundary), connected, homogeneous, and orientable, the paper establishes future C^0-inextendibility for spacetimes in this class. The result further extends to spacetimes possessing more than one regular black hole horizon.

Significance. If the adaptation holds, the result would extend C^0-inextendibility beyond the vacuum spherically symmetric case to non-vacuum models and geometries with more general fibres, providing a tool for analyzing the strong cosmic censorship conjecture in a wider setting of black hole spacetimes.

minor comments (1)
  1. The abstract states the fibre assumptions and the Kretschmann divergence condition but does not specify the precise warped-product metric ansatz or the exact statement of the adapted theorem from Sbierski; adding these would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their summary of the manuscript and for recognizing the potential extension of C^0-inextendibility results beyond the vacuum spherically symmetric case. The recommendation of 'uncertain' is noted, but no specific major comments were provided in the report. We are prepared to address any concrete concerns regarding the adaptation of Sbierski's proof if they are raised.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central result is obtained by adapting Sbierski's external C^0-inextendibility argument to a class of warped-product spacetimes once the fibre is assumed closed/connected/homogeneous/orientable and the Kretschmann scalar diverges at r=0. No equations or steps reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the derivation chain is self-contained against the cited external theorem and the explicitly listed geometric hypotheses.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The central claim rests on domain assumptions about the fibre geometry and the character of the singularity at r=0, plus the validity of adapting an external proof technique; no free parameters or invented entities are introduced in the abstract.

axioms (3)
  • domain assumption The fibre is closed (compact without boundary), connected, homogeneous, and orientable.
    Listed explicitly as suitable assumptions under which the result holds.
  • domain assumption The spacetime admits a singularity as r → 0 characterised by the divergence of the Kretschmann scalar.
    Defines the class of spacetimes considered and the nature of the singularity.
  • domain assumption The spacetimes are globally hyperbolic with a codimension-two Riemannian fibre and radial coordinate r serving as the warping function.
    Describes the structural properties of the warped-product class.

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Reference graph

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