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arxiv: 2607.02409 · v1 · pith:PZF6OXYOnew · submitted 2026-07-02 · 🌀 gr-qc

Black Hole Persistence in Scalar Tensor Theories

Balkar Yildirim , Alan Albert Coley This is my paper

Pith reviewed 2026-07-03 08:12 UTC · model grok-4.3

classification 🌀 gr-qc
keywords scalar-tensor gravityblack hole persistencecosmological bounceperturbative solutionsMcVittie geometryinhomogeneous spacetimesnonsingular cosmology
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The pith

A perturbative scalar-tensor model yields a small horizon that persists through a nonsingular cosmological bounce.

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

The paper develops a perturbative solution in scalar-tensor gravity that places a central inhomogeneity inside an evolving bouncing cosmological background. Leading order gives a flat radiation-dominated FLRW bounce, while first order introduces the inhomogeneity via a generalized McVittie geometry whose metric and scalar functions are expanded near the bounce. The resulting solution contains a small evolving horizon whose radius scales with the integration constant d0. This horizon remains present on both sides of the bounce and is interpreted as the surface of a surviving black hole. Its time evolution is asymmetric about the bounce time.

Core claim

In the perturbative scalar-tensor setup a generalized McVittie geometry is embedded at first order around a spatially flat bouncing FLRW background. The field equations are solved as a series in conformal time up to fourth order, producing a perfect-fluid solution with three arbitrary functions fixed by the requirement that the spacetime approach FLRW at large radii. With initial conditions that preserve the parabolic bounce, the constant d0 becomes the true small parameter and a horizon of size proportional to d0 appears. This horizon continues through the bounce without vanishing and its evolution is not symmetric about conformal time zero, supporting the interpretation that a black hole s

What carries the argument

First-order perturbative embedding of a generalized McVittie geometry into the scalar-tensor field equations on a radiation FLRW bounce, with the integration constant d0 serving as the effective perturbative parameter that controls the size of the central inhomogeneity and its horizon.

If this is right

  • The identified horizon evolves continuously through the bounce on both sides of conformal time zero.
  • The horizon's time dependence is asymmetric about the bounce.
  • All first-order perturbations vanish identically when the integration constant d0 is taken to zero.
  • The spacetime recovers the homogeneous FLRW solution at large radial distances once the three arbitrary functions are fixed by asymptotic matching.
  • The anisotropic fluid components satisfy the diagonal field equations at the orders considered.

Where Pith is reading between the lines

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

  • If the perturbative horizon survives in a fully nonlinear treatment, black-hole persistence could be a generic feature of bouncing cosmologies in scalar-tensor theories.
  • Global causal structure and trapped-surface analysis beyond the perturbative regime would be required to confirm the surface is a true event horizon rather than a local apparent horizon.
  • The same construction could be repeated with different matter contents or other classes of bounce solutions to test how robust the persistence result is.

Load-bearing premise

The generalized McVittie geometry can be consistently inserted at first perturbative order while satisfying the full scalar-tensor equations with an anisotropic fluid, and the resulting surface can be read as a black-hole horizon without additional global analysis.

What would settle it

An explicit computation showing that the apparent-horizon radius shrinks to zero exactly at the bounce or that the metric and scalar functions cease to solve the field equations at that instant would falsify the claimed persistence.

read the original abstract

We construct a perturbative scalar-tensor solution describing a central inhomogeneity embedded in an evolving cosmological background, with the aim of studying black hole persistence through a nonsingular bounce. Scalar-tensor gravity provides a natural framework for realizing bouncing cosmologies, while the inclusion of a localized inhomogeneity makes the field equations substantially more difficult to solve. We therefore adopt a perturbative scheme, with perturbative parameter $\epsilon$, in which the leading-order equations are solved by a spatially flat bouncing FLRW spacetime sourced by a radiation perfect fluid. At next order, a central inhomogeneity is introduced through a generalized McVittie geometry, with the perturbations encoded in the corresponding first-order metric and scalar-field functions. We first allow an anisotropic fluid with radial and tangential pressures, whose diagonal components solve the diagonal field equations. The field equations are solved as a series expansion up to $\mathcal{O}(\eta^4)$ near the bounce at $\eta=0$. The resulting perfect fluid solution contains three arbitrary functions which are constrained by requiring the spacetime to asymptote to FLRW as $r\to\infty$. With suitable initial conditions preserving the parabolic structure of the bounce, the integration constant $d_0$ emerges as the true perturbative parameter: all perturbations vanish as $d_0\to0$. Finally, we find a small evolving horizon, $r_h\sim d_0$, which we interpret as the horizon of the central inhomogeneity. Its persistence through the bounce supports the interpretation of a black hole surviving the cosmological transition, and its evolution is not symmetric about $\eta=0$.

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 / 1 minor

Summary. The paper constructs a perturbative scalar-tensor solution for a central inhomogeneity in a bouncing flat FLRW background using a generalized McVittie ansatz. At leading order the background is sourced by radiation; at O(ε) an anisotropic fluid is introduced whose diagonal pressures satisfy the diagonal field equations for the first-order metric and scalar perturbations, expanded to O(η^4) near the bounce. Asymptotic matching to FLRW fixes three arbitrary functions, d0 emerges as the controlling parameter, and a small evolving horizon r_h ~ d0 is identified that persists through η=0.

Significance. If the solution is internally consistent, the result supplies a concrete perturbative example of black-hole-like horizon persistence across a nonsingular bounce in scalar-tensor gravity, with potential implications for structure survival in bouncing cosmologies. The use of asymptotic boundary conditions and the reduction of the perturbative parameter to a single integration constant d0 are positive features of the approach.

major comments (2)
  1. [Abstract] Abstract: the construction states that an anisotropic fluid is chosen so that its diagonal pressures solve the diagonal field equations, but provides no verification that the off-diagonal components of the scalar-tensor equations vanish at O(ε). Because the central claim (persistence of the r_h ~ d0 horizon) requires the full set of equations to hold with this stress-energy, the absence of this check is load-bearing.
  2. [Abstract] Abstract: after introducing an anisotropic fluid, the text refers to the 'resulting perfect fluid solution'; this internal inconsistency in the stress-energy description must be clarified before the horizon interpretation can be assessed.
minor comments (1)
  1. The expansion is truncated at O(η^4); it is not shown whether higher-order terms in η alter the location or persistence of the reported horizon.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying points that require clarification. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the construction states that an anisotropic fluid is chosen so that its diagonal pressures solve the diagonal field equations, but provides no verification that the off-diagonal components of the scalar-tensor equations vanish at O(ε). Because the central claim (persistence of the r_h ~ d0 horizon) requires the full set of equations to hold with this stress-energy, the absence of this check is load-bearing.

    Authors: We acknowledge that the abstract does not explicitly address the off-diagonal components. The generalized McVittie ansatz and the perturbative expansion are constructed such that the symmetry ensures the off-diagonal equations are satisfied once the diagonal components are solved by the choice of anisotropic fluid; this follows from the form of the metric perturbations and the scalar field. To make the solution fully explicit, we will add a brief verification of the off-diagonal components in the revised manuscript. revision: yes

  2. Referee: [Abstract] Abstract: after introducing an anisotropic fluid, the text refers to the 'resulting perfect fluid solution'; this internal inconsistency in the stress-energy description must be clarified before the horizon interpretation can be assessed.

    Authors: We agree that the abstract contains inconsistent terminology. The fluid is introduced as anisotropic to solve the diagonal equations, but the resulting solution has equal radial and tangential pressures, reducing to a perfect fluid. We will revise the abstract and relevant sections to clarify this progression and use consistent language. revision: yes

Circularity Check

0 steps flagged

Minor reparameterization of integration constant; central persistence claim retains independent content from bounce solution

full rationale

The derivation begins with an exact FLRW bounce at leading order, introduces a generalized McVittie ansatz at O(ε), solves the diagonal field equations for an anisotropic fluid up to O(η^4), and imposes asymptotic FLRW matching to constrain three arbitrary functions. The subsequent choice of initial conditions that makes perturbations vanish as d0→0 simply identifies the remaining integration constant as the perturbative amplitude; this is a re-labeling rather than a reduction of the horizon-evolution result to the input. The reported asymmetry of rh(η) about η=0 and its survival through the bounce are outputs of the series solution under those constraints, not tautological. No self-citation chain, ansatz smuggling, or off-diagonal verification is presented as load-bearing in the supplied text, and the background bounce plus asymptotic conditions supply external structure. Hence only a minor (score-2) redefinition is present.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the choice of a radiation-dominated spatially flat bouncing FLRW background at zeroth order, the adoption of generalized McVittie at first order, and the perturbative expansion parameter d0 that is fixed by initial conditions rather than derived from first principles.

free parameters (1)
  • d0
    Integration constant that sets the amplitude of the central inhomogeneity and is promoted to the true perturbative parameter.
axioms (2)
  • domain assumption Leading-order solution is a spatially flat bouncing FLRW spacetime sourced by a radiation perfect fluid
    Stated as the zeroth-order background that the perturbation is built around.
  • domain assumption Generalized McVittie geometry can be used to encode the first-order central inhomogeneity
    Invoked to introduce the inhomogeneity while preserving asymptotic FLRW behavior.

pith-pipeline@v0.9.1-grok · 5806 in / 1520 out tokens · 28113 ms · 2026-07-03T08:12:22.271374+00:00 · methodology

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Reference graph

Works this paper leans on

36 extracted references · 22 canonical work pages · 16 internal anchors

  1. [1]

    Bouncing Cosmologies

    M. Novello and S. Bergliaffa, Phys. Rep.463, 127 (2008) [arXiv:0802.1634]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  2. [2]

    Tolman, Phys

    R.C. Tolman, Phys. Rev.38, 1758 (1931)

    1931

  3. [3]

    Lemaitre, Ann

    G. Lemaitre, Ann. Soc. Sci. Brux.53, 51 (1933)

    1933

  4. [4]

    Lemaitre, Gen

    G. Lemaitre, Gen. Rel. Grav.29, 641 (1997)

    1997

  5. [5]

    Lemaitre, Mon

    G. Lemaitre, Mon. Not. R. Astron. Soc.91, 490-501 (1931)

    1931

  6. [6]

    Turok, M

    N. Turok, M. Perry and P. J. Steinhardt, Phys. Rev. D70, 106004 (2004)

    2004

  7. [7]

    Veneziano, Europhys

    G. Veneziano, Europhys. Lett.2, 133 (1986)

    1986

  8. [8]

    Bojowald, Phys

    M. Bojowald, Phys. Rev. Lett.86, 5227 (2001); M. Bojowald, Phys. Rev. Lett.95, 091302 (2005); A. Ashtekar, T. Pawlowski and P. Singh, Phys. Rev. D74, 084003 (2006)

    2001

  9. [9]

    Ashtekar, inEinstein and the Changing Worldviews of Physics, ed

    A. Ashtekar, inEinstein and the Changing Worldviews of Physics, ed. C. Lehner, J. Renn and M. Schemmel, Springer, Berlin (2012)

    2012

  10. [10]

    Black hole formation in a contracting universe

    J. Quintin and R. Brandenberger, JCAP,11, 029 (2016) [arXiv:1609.02556]; Y-F. Cai, R. Bran- denburger and P. Peter (2013) [arXiv:1301.4703]; R. -G. Cai and A. Wang, Phys. Rev. D73, 063005 (2006); Y-F. Cai, W. Xue, R. Brandenburger and Zhang, (2009) [arXiv:0903.4938]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  11. [11]

    A Critical Review of Classical Bouncing Cosmologies

    D. Battefeld and P. Peter, Physics Reports571, 1 (2015) [arXiv:1406.2790]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  12. [12]

    Bouncing Cosmologies: Progress and Problems

    R. Brandenberger and P. Peter, Found. Phys.47, 6, 797-850 (2017) [arXiv:1603.05834]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  13. [13]

    Martin and P

    J. Martin and P. Peter, Phys. Rev. D68, 103517 (2003)

    2003

  14. [14]

    Non-singular cosmology in a model of non-relativistic gravity

    Y.F. Cai and E. N. Saridakis, JCAP10, 020 (2009) [arXiv:0906.1789]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  15. [15]

    Bahamonde et

    S. Bahamonde et al., Rep. Prog. Phys.86, 026901 (2023) [arXiv:2106.13793]

    work page arXiv 2023

  16. [16]

    The Matter Bounce Scenario in Loop Quantum Cosmology

    E. Wilson-Ewing, JCAP03, 026 (2013) [arXiv:1211.6269]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  17. [17]

    Arrows of Time in the Bouncing Universes of the No-boundary Quantum State

    J. Hartle and T. Hertog, (2012) [arXiv:1104.1733]. 16

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  18. [18]

    B. J. Carr and A. A. Coley, Int. J. Mod. Phys. D.20, 2733-2738 (2011); B. Carr, A. Coley and T. Clifton, (2017) [arXiv:1704.02919]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  19. [19]

    Clifton, B

    T. Clifton, B. Carr and A. Coley, Class. Quant. Grav.34, 135005 (2017); A. Coley, Class. Quant. Grav. 37, 245002 (2021) [arXiv:2012.14049]

    work page arXiv 2017

  20. [20]

    Beasts in Lambda-CDM Zoo

    B. Carr and J. Silk, Mon. Not. Roy. Astron. Soc.478, 3756-3775 (2018); M. Kawasaki and N. Kevlishvili, Nucl. Phys. B807, 229 (2009); A. D. Dolgov, (2016) [arXiv:1605.06749]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  21. [21]

    Pre-big-bang black-hole remnants and the past low entropy

    C. Rovelli and F, Vidotto, (2018) [arXiv:1805.03224]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  22. [22]

    Y. F. Cai, C. Tang, G. Mo, S. F. Yan, C. Chen, X. H. Ma, B. Wang, W. Luo, D. A. Easson and A. Marciano, Sci. China Phys. Mech. Astron.67, 259512 (2024) [arXiv:2301.09403]

    work page arXiv 2024

  23. [23]

    Corman, W

    M. Corman, W. E. East and J. L. Ripley, JCAP09, 063 (2022) [arXiv:2206.08466]

    work page arXiv 2022

  24. [24]

    P´ erez and G

    D. P´ erez and G. E. Romero, Phys. Rev. D105, 104047 (2022), [arXiv:2205.10333]

    work page arXiv 2022

  25. [25]

    G. C. McVittie, Mon. Not. Roy. Astron. Soc.93, 325 (1933)

    1933

  26. [26]

    B. C. Nolan, Phys. Rev. D58, 064006 (1998) [arXiv:gr-qc/9805041];ibid.Class. Quant. Grav. 16, 1227 (1999) ;ibid.Class. Quant. Grav.16, 3183 (1999) [arXiv:gr-qc/9907018];ibid.. Class. Quant. Grav.,34, 225002 (2017);ibid., Class. Quant. Grav.16(1999) ;ibid., Class. Quant. Grav. 42, 235019 (2025) [arXiv:2509.18903]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  27. [27]

    Existence of black holes in Friedmann-Robertson-Walker universe dominated by dark energy

    Z.-H. Li and A. Wang, Mod. Phys. Lett. A22, 1663 (2007) [arXiv:astro-ph/0607554]; N. Kaloper, M. Kleban and D. Martin, Phys. Rev. D81, 104044 (2010) [arXiv:1003.4777]; R.A. Sussman, Gen. Relativ. Gravit.17, 251 (1985) ; V. Faraoni and M. Rinaldi, Phys. Rev. D110, 063553 (2024) [arXiv:2407.14549]; L. Modesto and E. Rattu, (2025) [arXiv:2510.04165]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  28. [28]

    A non inflationary model with scale invariant cosmological perturbations

    P. Peter, E. J. C. Pinho, and N. Pinto-Neto, Phys. Rev. D75(2007) [arXiv:hep-th/0610205]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  29. [29]

    Quantum cosmology from the de Broglie-Bohm perspective

    N. Pinto-Neto and J. C. Fabris, Class. Quant. Grav.30, 143001 (2013) [arXiv:1306.0820]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  30. [30]

    Cosmological expansion and local physics

    V. Faraoni and A. Jacques, Phys. Rev. D76(2007) [arXiv:0707.1350]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  31. [31]

    McVittie's Legacy: Black Holes in an Expanding Universe

    N. Kaloper, M. Kleban, and D. Martin, Phys. Rev. D81(2010) [arXiv:1003.4777]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  32. [32]

    P´ erez, S

    D. P´ erez, S. E. P. Bergliaffa, and G. E. Romero, Phys. Rev. D103(2021) [arXiv:2103.00108]

    work page arXiv 2021

  33. [33]

    Yildirim, A

    B. Yildirim, A. A. Coley, and D. F. L´ opez, Gen. Relativ. Gravit.58, 42 (2026)

    2026

  34. [34]

    J. D. Barrow, Phys. Rev. D48, 3592 (1933)

    1933

  35. [35]

    J. D. Barrow, Phys. Rev. D47, 5329 (1993)

    1993

  36. [36]

    Faraoni, Cosmology in Scalar-Tensor Gravity (2004) 17

    V. Faraoni, Cosmology in Scalar-Tensor Gravity (2004) 17

    2004