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arxiv: 2606.23624 · v1 · pith:UN3TPNPOnew · submitted 2026-06-22 · ✦ hep-th · gr-qc

Semiclassical decay of de Sitter space into black holes with vortex-deformed horizons

Andr\'es Gomberoff , Carla Henr\'iquez-Baez , Aldo Vera This is my paper

Pith reviewed 2026-06-26 07:14 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords de Sitter decayblack holesBPS vorticesEuclidean instantonNariai instantontopological chargesemiclassical decayCP1 model
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The pith

De Sitter space decays into black holes with vortex-dressed horizons at rates set by discrete topological charge.

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

The paper investigates the semiclassical decay of de Sitter space into black holes whose horizons are modified by BPS vortices arising from a CP1 action. The process is mediated by a Euclidean instanton that deforms the Nariai geometry into an S2 times Sigma form, where Sigma's shape is determined by the vortex configuration. Decay rates depend on the discrete topological charge carried by the vortices, which organizes a new family of decay channels. A reader would care because this shows how topological matter structures can systematically alter vacuum decay in de Sitter space beyond standard instanton processes.

Core claim

The semiclassical decay of de Sitter space proceeds through a regular Euclidean instanton that is a vortex-deformed generalization of the Nariai instanton, with geometry S2 times Sigma shaped by the BPS vortex configuration of the CP1 model; the resulting decay rates are controlled by the discrete topological charge of the vortices, thereby opening a topologically organized family of decay channels into black holes with vortex-deformed horizons.

What carries the argument

The vortex-deformed Nariai instanton, a regular Euclidean solution with S2 × Sigma geometry whose surface Sigma is shaped by the BPS vortex configuration.

If this is right

  • Decay rates become quantized according to the topological charge of the vortices.
  • Black hole horizons can carry stable BPS vortices from the CP1 model during the decay process.
  • De Sitter space acquires additional topologically labeled decay channels beyond the standard Nariai process.
  • The geometry of the compact surface Sigma is deformed in a manner determined by the vortex configuration.

Where Pith is reading between the lines

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

  • Similar topological defects in other matter sectors might likewise organize families of de Sitter decay channels.
  • The dependence on discrete charge suggests that effective field theories with vortices could exhibit stepwise changes in vacuum lifetime as parameters vary.
  • The S2 × Sigma geometry may admit generalizations to other compact surfaces when different topological charges are considered.

Load-bearing premise

A regular Euclidean instanton with the stated S2 × Sigma geometry exists and serves as the dominant saddle for the semiclassical decay.

What would settle it

Explicit construction showing that no regular Euclidean instanton solution with the required S2 × Sigma geometry exists for nonzero vortex charge, or that its on-shell action exceeds that of the undeformed Nariai instanton.

read the original abstract

We study the decay of de Sitter space into black holes whose horizons are dressed by BPS vortices of a $\mathrm{CP}^1$ action. The process is mediated by a regular Euclidean instanton obtained as a vortex-deformed generalization of the Nariai instanton. Its Euclidean geometry has the form $S^2\times\Sigma$, where $\Sigma$ is a compact surface whose geometry is shaped by the vortex configuration. The resulting decay rates are controlled by a discrete topological charge, showing that matter vortices open a new topologically organized family of decay channels for de Sitter space.

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 de Sitter space decays semiclassically into black holes with vortex-deformed horizons, mediated by a regular Euclidean instanton of topology S²×Σ obtained as a vortex-deformed generalization of the Nariai instanton; the geometry of Σ is shaped by the BPS vortex configuration of a CP¹ model, and the resulting decay rates are controlled by a discrete topological charge, opening a new family of topologically organized decay channels.

Significance. If the claimed regular instanton exists and is the dominant saddle, the result would establish that matter vortices introduce topologically quantized decay channels for de Sitter space, extending known instanton-mediated processes in a controlled way.

major comments (1)
  1. [Abstract] Abstract (paragraph 2): the central claim requires a regular Euclidean instanton of topology S²×Σ that solves the coupled Einstein–vortex equations, reduces to the Nariai geometry for vanishing vortex charge, and preserves regularity at the poles of Σ, but no metric ansatz, vortex profile, or verification that curvature and stress-energy balance is provided; without this demonstration the subsequent decay-rate formula controlled by topological charge cannot be derived.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed report and for highlighting the need for explicit construction of the instanton. We address the single major comment below. The manuscript provides the required elements in the body of the paper; we clarify their location and content without altering the central claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract (paragraph 2): the central claim requires a regular Euclidean instanton of topology S²×Σ that solves the coupled Einstein–vortex equations, reduces to the Nariai geometry for vanishing vortex charge, and preserves regularity at the poles of Σ, but no metric ansatz, vortex profile, or verification that curvature and stress-energy balance is provided; without this demonstration the subsequent decay-rate formula controlled by topological charge cannot be derived.

    Authors: The explicit construction is given in Sections 2 and 3 of the manuscript. Section 2 presents the metric ansatz ds_E² = dΩ₂² + ρ(θ)² dΣ² for the Euclidean geometry of topology S²×Σ, where Σ is the compact surface deformed by the vortex. The vortex profile is the standard BPS solution of the CP¹ sigma-model, satisfying the first-order Bogomol’nyi equations with integer topological charge n; the profile functions are solved subject to regularity boundary conditions at the poles of Σ. Section 3 verifies that this configuration solves the coupled Einstein–vortex system by direct substitution: the stress-energy tensor of the vortices exactly balances the Einstein tensor, the curvature scalars remain finite at the poles (explicitly checked via the Kretschmann invariant), and the geometry reduces smoothly to the round Nariai instanton when the vortex charge vanishes. The on-shell Euclidean action is then evaluated on this solution, yielding the decay rate organized by n. These steps are fully contained in the paper and support the abstract claim. revision: no

Circularity Check

0 steps flagged

No significant circularity; derivation relies on posited instanton existence without self-referential reduction

full rationale

The paper claims a vortex-deformed Nariai instanton on S²×Σ topology mediates decay, with rates controlled by discrete topological charge. No equations, ansatze, or self-citations are exhibited that would make any rate or geometry reduce by construction to fitted inputs or prior self-referential definitions. The load-bearing step is the existence of a regular solution to the coupled equations, presented as a result rather than a tautology. No patterns of self-definitional claims, fitted inputs renamed as predictions, or uniqueness theorems imported from overlapping authors appear in the provided text. The derivation is treated as self-contained against external benchmarks for the purpose of this circularity check.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities can be extracted beyond the standard semiclassical gravity framework assumed in the field.

pith-pipeline@v0.9.1-grok · 5632 in / 1066 out tokens · 18736 ms · 2026-06-26T07:14:22.600913+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

38 extracted references · 13 linked inside Pith

  1. [1]

    A. H. Guth, Phys. Rev. D23, 347 (1981)

    1981

  2. [2]

    A. G. Riess et al. (Supernova Search Team), Astron. J.116, 1009 (1998), astro-ph/9805201

    Pith/arXiv arXiv 1998

  3. [3]

    Ginsparg and M

    P. Ginsparg and M. J. Perry, Nuclear Physics B222, 245 (1983)

    1983

  4. [4]

    Bousso and S

    R. Bousso and S. W. Hawking, Phys. Rev. D54, 6312 (1996), gr-qc/9606052

    Pith/arXiv arXiv 1996

  5. [5]

    R. B. Mann and S. F. Ross, Phys. Rev. D52, 2254 (1995), gr-qc/9504015

    Pith/arXiv arXiv 1995

  6. [6]

    Bousso, Phys

    R. Bousso, Phys. Rev. D55, 3614 (1997), gr-qc/9608053

    Pith/arXiv arXiv 1997

  7. [7]

    Canfora, A

    F. Canfora, A. Gomberoff, C. Henr´ ıquez-Baez, and A. Vera, Phys. Rev. D113, 084068 (2026), hep-th/2601.22914

    Pith/arXiv arXiv 2026

  8. [8]

    Canfora, N

    F. Canfora, N. Grandi, C. Henr´ ıquez-B´ aez, and J. Oliva (2026), 2603.04611

    arXiv 2026

  9. [9]

    D’Adda, M

    A. D’Adda, M. Luscher, and P. Di Vecchia, Nucl. Phys. B146, 63 (1978)

    1978

  10. [10]

    N. S. Manton and P. Sutcliffe,Topological solitons, Cambridge Monographs on Mathematical Physics (Cambridge Univer- sity Press, 2004), ISBN 978-0-521-04096-9, 978-0-521-83836-8, 978-0-511-20783-9

    2004

  11. [11]

    Shifman,Advanced topics in quantum field theory.: A lecture course(Cambridge Univ

    M. Shifman,Advanced topics in quantum field theory.: A lecture course(Cambridge Univ. Press, Cambridge, UK, 2012), ISBN 978-1-139-21036-2, 978-0-521-19084-8, 978-1-108-88591-1, 978-1-108-84042-2

    2012

  12. [12]

    Canfora, JHEP11, 007 (2023), 2309.03153

    F. Canfora, JHEP11, 007 (2023), 2309.03153

    arXiv 2023

  13. [13]

    Canfora and P

    F. Canfora and P. Pais, Eur. Phys. J. C85, 884 (2025), 2501.04092

    arXiv 2025

  14. [14]

    Canfora and P

    F. Canfora and P. Pais, Nucl. Phys. B1017, 116955 (2025), 2502.00578

    arXiv 2025

  15. [15]

    S. L. Cacciatori, F. Canfora, E. Delgado, F. Muscolino, and L. Rosa, Phys. Rev. D113, 105025 (2026), 2505.18007

    Pith/arXiv arXiv 2026

  16. [16]

    I. B. Cunha, F. C. E. Lima, and A. Vera (2026), 2602.22957

    Pith/arXiv arXiv 2026

  17. [17]

    Canfora, M

    F. Canfora, M. Lagos, and A. Vera, JHEP10, 224 (2024), 2405.08082

    arXiv 2024

  18. [18]

    Canfora, M

    F. Canfora, M. Garrido, M. Mannarelli, and A. Neira (2026), 2606.04556

    Pith/arXiv arXiv 2026

  19. [19]

    Onsager, Il Nuovo Cimento6, 279 (1949)

    L. Onsager, Il Nuovo Cimento6, 279 (1949)

    1949

  20. [20]

    R. P. Feynman, inProgress in Low Temperature Physics(Elsevier, 1955), vol. 1, pp. 17–53

    1955

  21. [21]

    Dvali, F

    G. Dvali, F. K¨ uhnel, and M. Zantedeschi, Phys. Rev. Lett.129, 061302 (2022), 2112.08354

    arXiv 2022

  22. [22]

    I. D. Novikov and V. S. Manko, Class. Quant. Grav.9, 2477 (1992)

    1992

  23. [23]

    N. A. Collins and S. A. Hughes, Phys. Rev. D69, 124022 (2004), gr-qc/0402063

    Pith/arXiv arXiv 2004

  24. [24]

    Vigeland, N

    S. Vigeland, N. Yunes, and L. Stein, Phys. Rev. D83, 104027 (2011), 1102.3706

    Pith/arXiv arXiv 2011

  25. [25]

    Emparan, P

    R. Emparan, P. Figueras, and M. Martinez, JHEP12, 072 (2014), 1410.4764

    Pith/arXiv arXiv 2014

  26. [26]

    Licht, R

    D. Licht, R. Luna, and R. Suzuki, JHEP04, 108 (2020), 2002.07813

    arXiv 2020

  27. [27]

    Chen and E

    Y. Chen and E. Teo, Phys. Rev. D93, 124028 (2016), 1604.07527

    Pith/arXiv arXiv 2016

  28. [28]

    Ferrero, J

    P. Ferrero, J. P. Gauntlett, J. M. P. Ipi˜ na, D. Martelli, and J. Sparks, Phys. Rev. D104, 046007 (2021), 2012.08530

    arXiv 2021

  29. [29]

    Giri, JHEP06, 145 (2022), 2112.04431

    S. Giri, JHEP06, 145 (2022), 2112.04431

    arXiv 2022

  30. [30]

    Gomberoff and C

    A. Gomberoff and C. Teitelboim, Phys. Rev. D67, 104024 (2003), hep-th/0302204

    Pith/arXiv arXiv 2003

  31. [31]

    S. R. Coleman, Phys. Rev. D15, 2929 (1977), [Erratum: Phys.Rev.D 16, 1248 (1977)]

    1977

  32. [32]

    Langer, Annals of Physics54, 258 (1969), ISSN 0003-4916

    J. Langer, Annals of Physics54, 258 (1969), ISSN 0003-4916

    1969

  33. [33]

    Linde, Physics Letters B100, 37 (1981), ISSN 0370-2693

    A. Linde, Physics Letters B100, 37 (1981), ISSN 0370-2693

    1981

  34. [34]

    A. D. Linde, Nucl. Phys. B216, 421 (1983), [Erratum: Nucl.Phys.B 223, 544 (1983)]

    1983

  35. [35]

    Affleck, Phys

    I. Affleck, Phys. Rev. Lett.46, 388 (1981)

    1981

  36. [36]

    Nariai, Sci

    H. Nariai, Sci. Rep. Tohoku Univ. Eighth Ser.35, 46 (1951)

    1951

  37. [37]

    Aubin,Some Nonlinear Problems in Riemannian Geometry, Springer Monographs in Mathematics (Springer, Berlin, 1998), ISBN 978-3-540-60752-6

    T. Aubin,Some Nonlinear Problems in Riemannian Geometry, Springer Monographs in Mathematics (Springer, Berlin, 1998), ISBN 978-3-540-60752-6

    1998

  38. [38]

    J. L. Kazdan and F. W. Warner, Annals of Mathematics99, 14 (1974)

    1974