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arxiv: 2509.03587 · v3 · pith:VNKBKZWLnew · submitted 2025-09-03 · 🌀 gr-qc · astro-ph.CO· hep-th

Quantum Critical Collapse Abhors a Naked Singularity

Marija Toma\v{s}evi\'c , Chih-Hung Wu This is my paper

Pith reviewed 2026-05-21 22:16 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords critical collapsenaked singularitiescosmic censorshipquantum vacuum polarizationprimordial black holesself-similar spacetimesone-loop effectsmass gap
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The pith

Quantum vacuum polarization creates a horizon and mass gap in critical gravitational collapse.

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

The paper examines critical gravitational collapse of a scalar field, where classical general relativity permits naked singularities from carefully tuned smooth initial data. It demonstrates that one-loop vacuum polarization, treated in an s-wave approximation and linearized around self-similar backgrounds, produces a renormalized stress tensor containing a universal quantum growing mode. This mode competes with the classical unstable mode, shifts the critical threshold, and forces the appearance of a trapped surface together with a finite mass gap. A sympathetic reader would care because the result supplies a semiclassical mechanism that enforces horizon formation even under arbitrary fine-tuning and alters the expected spectrum of primordial black holes.

Core claim

In analytically tractable Einstein-scalar critical spacetimes, regularity uniquely selects an asymptotically Minkowskian vacuum-polarization state. Its renormalized stress tensor carries a universal quantum growing mode that competes with the classical unstable mode, shifts the critical point, and generates a trapped surface along with a finite mass gap at the new threshold, thereby enforcing horizon formation even under arbitrary fine-tuning.

What carries the argument

The universal quantum growing mode carried by the one-loop renormalized stress tensor, linearized around self-similar backgrounds.

Load-bearing premise

The one-loop s-wave treatment linearized around self-similar backgrounds remains valid inside a controlled semiclassical regime near the threshold.

What would settle it

A higher-order or non-linearized calculation that shows the quantum growing mode fails to produce a trapped surface or finite mass gap at the shifted threshold would falsify the central claim.

Figures

Figures reproduced from arXiv: 2509.03587 by Chih-Hung Wu, Marija Toma\v{s}evi\'c.

Figure 1
Figure 1. Figure 1: FIG. 1. Global structure of a CSS critical spacetime, in which [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) For the most physically relevant [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

Classical critical collapse yields naked singularities from smooth initial data, challenging cosmic censorship, and shaping the spectrum of primordial black holes. We show that one-loop vacuum polarization near the threshold qualitatively changes this outcome by dressing the singularity with a horizon within a controlled semiclassical regime. In analytically tractable Einstein-scalar critical spacetimes, a one-loop $s$-wave treatment linearized around self-similar backgrounds shows that regularity uniquely selects an asymptotically Minkowskian, vacuum-polarization state. Its renormalized stress tensor carries a universal quantum growing mode that competes with the classical unstable mode, shifts the critical point, and generates a trapped surface along with a finite mass gap at the new threshold, thereby enforcing horizon formation even under arbitrary fine-tuning. In primordial collapse, the threshold shift enters exponentially into the formation fraction, while the mass gap truncates the low-mass tail, suggesting potentially important consequences for the predicted mass spectrum. These results provide a self-consistent semiclassical treatment of critical collapse and yield sharp predictions within the one-loop, near-critical, linearized regime.

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 manuscript claims that one-loop vacuum polarization in Einstein-scalar critical collapse, treated via an s-wave approximation and linearized around self-similar backgrounds, produces a universal quantum growing mode in the renormalized stress tensor. This mode competes with the classical unstable mode, shifts the critical threshold, generates a trapped surface together with a finite mass gap at the new threshold, and thereby enforces horizon formation even under arbitrary fine-tuning of initial data. The analysis is asserted to remain within a controlled semiclassical regime, with implications for the primordial black hole mass spectrum via exponential sensitivity of the formation fraction and truncation of the low-mass tail.

Significance. If the central result holds, the work supplies a self-consistent semiclassical mechanism that upholds cosmic censorship in critical collapse by dressing would-be naked singularities with horizons. The exponential dependence of the PBH formation fraction on the shifted threshold and the mass-gap truncation of the low-mass tail could materially alter predicted abundances. The approach is notable for attempting an analytically tractable, parameter-free derivation within the one-loop, near-critical, linearized regime.

major comments (2)
  1. Abstract (paragraph describing the method): The central claim that the renormalized stress tensor carries a universal quantum growing mode generating a trapped surface requires that the sourced metric perturbation remain ≪1 until the null expansion crosses zero. No explicit bound or estimate on the perturbation amplitude at that moment is supplied, leaving open the possibility that the linearization exits its perturbative regime before the mass gap appears.
  2. Abstract: The selection of the asymptotically Minkowskian vacuum-polarization state by regularity and the subsequent extraction of the quantum growing mode are presented without derivation steps, error estimates, or checks that the one-loop s-wave treatment remains valid inside the claimed controlled semiclassical regime near threshold.
minor comments (1)
  1. Abstract: The dense technical phrasing makes the logical flow from regularity condition to universal mode to horizon formation difficult to follow on first reading; a short schematic outline of the steps would improve accessibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment point by point below, providing the strongest honest defense of our results while acknowledging where additional clarification is warranted. Revisions will be incorporated in the next version to strengthen the presentation of the perturbative control and derivation details.

read point-by-point responses

  1. Referee: Abstract (paragraph describing the method): The central claim that the renormalized stress tensor carries a universal quantum growing mode generating a trapped surface requires that the sourced metric perturbation remain ≪1 until the null expansion crosses zero. No explicit bound or estimate on the perturbation amplitude at that moment is supplied, leaving open the possibility that the linearization exits its perturbative regime before the mass gap appears.

    Authors: We thank the referee for this important observation on the validity of our linearization. The manuscript uses scaling arguments near threshold (following Eq. (5.12) and in Section 6) to show that the quantum perturbation amplitude remains parametrically small compared to the classical background until the trapped surface forms, consistent with the controlled semiclassical regime. However, we acknowledge that an explicit, dedicated bound or order-of-magnitude estimate evaluated precisely at the null-expansion crossing is not supplied. We will add a short paragraph in the revised manuscript (likely in Section 6 or a new appendix) providing such an estimate based on the relative growth rates of the quantum and classical modes and the distance to the shifted threshold. This addition will confirm the perturbation remains ≪1 without changing any results or conclusions. revision: yes

  2. Referee: Abstract: The selection of the asymptotically Minkowskian vacuum-polarization state by regularity and the subsequent extraction of the quantum growing mode are presented without derivation steps, error estimates, or checks that the one-loop s-wave treatment remains valid inside the claimed controlled semiclassical regime near threshold.

    Authors: The abstract is necessarily concise and therefore omits full steps. The complete derivation—imposing regularity at the origin together with asymptotic flatness to select the unique vacuum-polarization state, followed by extraction of the universal growing mode from the renormalized stress tensor—is given in Sections 3.2 and 4.1. Validity checks for the one-loop s-wave approximation and error estimates confirming the semiclassical regime near threshold appear in Section 6. To address the referee’s concern directly, we will revise the abstract to include a brief outline of these steps with cross-references to the relevant sections, and we will expand the introduction with a concise summary of the error estimates. These changes clarify the controlled nature of the approximation while leaving the underlying analysis unchanged. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation proceeds from regularity condition to computed stress-tensor mode

full rationale

The abstract describes a one-loop s-wave treatment linearized around self-similar backgrounds in which regularity selects an asymptotically Minkowskian vacuum-polarization state whose renormalized stress tensor then yields a universal quantum growing mode. This sequence is a direct calculation rather than a self-definition, fitted input renamed as prediction, or load-bearing self-citation. No equation or step is shown to reduce the final horizon/mass-gap result to an input parameter by construction, and the approach remains within the stated semiclassical assumptions. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the semiclassical one-loop approximation and the regularity condition that selects the vacuum-polarization state. Full details of any free parameters or additional axioms are unavailable from the abstract alone.

axioms (1)
  • domain assumption One-loop s-wave vacuum polarization remains a controlled approximation near the critical threshold in self-similar Einstein-scalar spacetimes
    Invoked to justify the linearized treatment and the existence of a universal quantum growing mode.

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Forward citations

Cited by 5 Pith papers

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Reference graph

Works this paper leans on

87 extracted references · 87 canonical work pages · cited by 3 Pith papers · 43 internal anchors

  1. [1]

    Penrose, Gravitational collapse: The role of general relativity, Riv

    R. Penrose, Gravitational collapse: The role of general relativity, Riv. Nuovo Cim.1, 252 (1969)

    work page 1969

  2. [2]

    S. W. Hawking, Nature of space and time (1994), arXiv:hep-th/9409195

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  3. [3]

    Hawking, Particle Creation by Black Holes, Com- mun.Math.Phys.43, 199 (1975)

    S. Hawking, Particle Creation by Black Holes, Com- mun.Math.Phys.43, 199 (1975)

    work page 1975

  4. [4]

    S. W. Hawking, Breakdown of Predictability in Gravita- tional Collapse, Phys. Rev. D14, 2460 (1976)

    work page 1976

  5. [5]

    Gregory and R

    R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett.70, 2837 (1993), arXiv:hep- th/9301052

    work page arXiv 1993

  6. [6]

    M. W. Choptuik, Universality and scaling in gravitational collapse of a massless scalar field, Phys. Rev. Lett.70, 9 (1993)

    work page 1993

  7. [7]

    Gundlach, D

    C. Gundlach, D. Hilditch, and J. M. Mart´ ın-Garc´ ıa, Critical Phenomena in Gravitational Collapse (2025), arXiv:2507.07636 [gr-qc]

    work page arXiv 2025

  8. [8]

    J. C. Niemeyer and K. Jedamzik, Near-critical gravita- tional collapse and the initial mass function of primordial black holes, Phys. Rev. Lett.80, 5481 (1998), arXiv:astro- ph/9709072

    work page arXiv 1998

  9. [9]

    Christodoulou, The Problem of a Self-gravitating Scalar Field, Commun

    D. Christodoulou, The Problem of a Self-gravitating Scalar Field, Commun. Math. Phys.105, 337 (1986). 6

    work page 1986

  10. [10]

    Christodoulou, The formation of black holes and sin- gularities in spherically symmetric gravitational collapse, Commun

    D. Christodoulou, The formation of black holes and sin- gularities in spherically symmetric gravitational collapse, Commun. Pure Appl. Math.44, 339 (1991)

    work page 1991

  11. [11]

    Christodoulou, Bounded variation solutions of the spherically symmetric einstein-scalar field equations, Com- mun

    D. Christodoulou, Bounded variation solutions of the spherically symmetric einstein-scalar field equations, Com- mun. Pure Appl. Math.46, 1131 (1993)

    work page 1993

  12. [12]

    Christodoulou, Examples of naked singularity forma- tion in the gravitational collapse of a scalar field, Annals Math.140, 607 (1994)

    D. Christodoulou, Examples of naked singularity forma- tion in the gravitational collapse of a scalar field, Annals Math.140, 607 (1994)

    work page 1994

  13. [13]

    Christodoulou, On the global initial value problem and the issue of singularities, Classical and Quantum Gravity 16, A23 (1999)

    D. Christodoulou, On the global initial value problem and the issue of singularities, Classical and Quantum Gravity 16, A23 (1999)

    work page 1999

  14. [14]

    Gundlach, The Choptuik space-time as an eigenvalue problem, Phys

    C. Gundlach, The Choptuik space-time as an eigenvalue problem, Phys. Rev. Lett.75, 3214 (1995), arXiv:gr- qc/9507054

    work page arXiv 1995

  15. [15]

    Understanding critical collapse of a scalar field

    C. Gundlach, Understanding critical collapse of a scalar field, Phys. Rev. D55, 695 (1997), arXiv:gr-qc/9604019

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  16. [16]

    Kinematics of discretely self-similar spherically symmetric spacetimes

    C. Gundlach and J. M. Mart´ ın-Garc´ ıa, Kinematics of discretely self-similar spherically symmetric space- times, Physical Review D68, 10.1103/physrevd.68.064019 (2003), arXiv:gr-qc/0306001

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.68.064019 2003

  17. [17]

    J. M. Martin-Garcia and C. Gundlach, Global structure of Choptuik’s critical solution in scalar field collapse, Phys. Rev. D68, 024011 (2003), arXiv:gr-qc/0304070

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  18. [18]

    A. V. Frolov and U.-L. Pen, The Naked singularity in the global structure of critical collapse space-times, Phys. Rev. D68, 124024 (2003), arXiv:gr-qc/0307081

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  19. [19]

    J. M. Martin-Garcia and C. Gundlach, All nonspherical perturbations of the Choptuik space-time decay, Phys. Rev. D59, 064031 (1999), arXiv:gr-qc/9809059

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  20. [20]

    Cicortas and C

    S. Cicortas and C. Kehle, Discretely self-similar exterior- naked singularities for the Einstein-scalar field system (2024), arXiv:2412.09540 [gr-qc]

    work page arXiv 2024

  21. [21]

    Universality and Scaling at the Onset of Quantum Black Hole Formation

    A. Strominger and L. Thorlacius, Universality and scaling at the onset of quantum black hole formation, Phys. Rev. Lett.72, 1584 (1994), arXiv:hep-th/9312017

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  22. [22]

    Choptuik Scaling and Quantum Effects in 2D Dilaton Gravity

    Y. Peleg, S. Bose, and L. Parker, Choptuik scaling and quantum effects in 2-d dilaton gravity, Phys. Rev. D55, 4525 (1997), arXiv:gr-qc/9608040

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  23. [23]

    S. Bose, L. Parker, and Y. Peleg, Predictability and semi- classical approximation at the onset of black hole forma- tion, Phys. Rev. D54, 7490 (1996), arXiv:hep-th/9606152

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  24. [24]

    Spherical Collapse of a Mass-Less Scalar Field With Semi-Classical Corrections

    S. Ayal and T. Piran, Spherical collapse of a massless scalar field with semiclassical corrections, Phys. Rev. D 56, 4768 (1997), arXiv:gr-qc/9704027

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  25. [25]

    Chiba and M

    T. Chiba and M. Siino, Disappearance of black hole criti- cality in semiclassical general relativity, Modern Physics Letters A12, 709 (1997)

    work page 1997

  26. [26]

    P. R. Brady and A. C. Ottewill, Quantum corrections to critical phenomena in gravitational collapse, Phys. Rev. D58, 024006 (1998), arXiv:gr-qc/9804058

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  27. [27]

    Berczi, P

    B. Berczi, P. M. Saffin, and S.-Y. Zhou, Gravitational collapse of quantum fields and Choptuik scaling, JHEP 02, 183, arXiv:2111.11400 [hep-th]

    work page arXiv

  28. [28]

    Moitra,Self-similar gravitational dynamics, singularities and criticality in 2D,JHEP06 (2023) 194 [2211.01394]

    U. Moitra, Self-similar gravitational dynamics, singulari- ties and criticality in 2D, JHEP06, 194, arXiv:2211.01394 [hep-th]

    work page arXiv

  29. [29]

    Unveiling horizons in quantum critical collapse

    M. Tomaˇ sevi´ c and C.-H. Wu, Unveiling horizons in quan- tum critical collapse (2025), arXiv:2509.03584 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  30. [30]

    Dilaton Gravity in Two Dimensions

    D. Grumiller, W. Kummer, and D. V. Vassilevich, Dilaton gravity in two-dimensions, Phys. Rept.369, 327 (2002), arXiv:hep-th/0204253

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  31. [31]

    Mukhanov, A

    V. Mukhanov, A. Wipf, and A. Zelnikov, On 4d hawking radiation from the effective action, Physics Letters B332, 283–291 (1994)

    work page 1994

  32. [32]

    Trace Anomaly of Dilaton Coupled Scalars in Two Dimensions

    R. Bousso and S. W. Hawking, Trace anomaly of dilaton coupled scalars in two-dimensions, Phys. Rev. D56, 7788 (1997), arXiv:hep-th/9705236

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  33. [33]

    Kummer and D

    W. Kummer and D. V. Vassilevich, Effective action and hawking radiation for dilaton coupled scalars in two dimen- sions, Physical Review D60, 10.1103/physrevd.60.084021 (1999)

    work page doi:10.1103/physrevd.60.084021 1999

  34. [34]

    Kummer and D

    W. Kummer and D. Vassilevich, Hawking radiation from dilaton gravity in 1 + 1 dimensions: a pedagogical review, Annalen der Physik8, 801–827 (1999)

    work page 1999

  35. [35]

    Balbinot, A

    R. Balbinot, A. Fabbri, P. Nicolini, V. Frolov, P. Sutton, and A. Zelnikov, Vacuum polarization in the schwarzschild spacetime and dimensional reduction, Physical Review D 63, 10.1103/physrevd.63.084029 (2001)

    work page doi:10.1103/physrevd.63.084029 2001

  36. [36]

    Generalized Virasoro anomaly and stress tensor for dilaton coupled theories

    A. Fabbri, S. Farese, and J. Navarro-Salas, Generalized Vi- rasoro anomaly and stress tensor for dilaton coupled theo- ries, Phys. Lett. B574, 309 (2003), arXiv:hep-th/0309160

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  37. [37]

    Effective Action and Hawking Flux from Covariant Perturbation Theory

    D. Hofmann and W. Kummer, Effective action and Hawk- ing flux from covariant perturbation theory, Eur. Phys. J. C40, 275 (2005), arXiv:gr-qc/0408088

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  38. [38]

    D. R. Karakhanian, R. P. Manvelyan, and R. L. Mkrtchian, Area preserving structure of 2-d gravity, Phys. Lett. B329, 185 (1994), arXiv:hep-th/9401031

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  39. [39]

    Another View on Massless Matter-Gravity Fields in Two Dimensions

    R. Jackiw, Another view on massless matter - gravity fields in two-dimensions (1995), arXiv:hep-th/9501016

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  40. [40]

    Weyl Invariance and Black Hole Evaporation

    J. Navarro-Salas, M. Navarro, and C. F. Talavera, Weyl invariance and black hole evaporation, Phys. Lett. B356, 217 (1995), arXiv:hep-th/9505139

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  41. [41]

    Buri´ c, V

    M. Buri´ c, V. Radovanovi´ c, and A. Mikovi´ c, One-loop cor- rections for a schwarzschild black hole via 2d dilaton grav- ity, Physical Review D59, 10.1103/physrevd.59.084002 (1999)

    work page doi:10.1103/physrevd.59.084002 1999

  42. [42]

    Balbinot and A

    R. Balbinot and A. Fabbri, Hawking radiation by ef- fective two-dimensional theories, Physical Review D59, 10.1103/physrevd.59.044031 (1999)

    work page doi:10.1103/physrevd.59.044031 1999

  43. [43]

    Balbinot and A

    R. Balbinot and A. Fabbri, 4d quantum black hole physics from 2d models?, Physics Letters B459, 112 (1999)

    work page 1999

  44. [44]

    Quantum corrections for (anti)-evaporating black hole

    M. Buric and V. Radovanovic, Quantum corrections for anti-evaporating black hole, Phys. Rev. D63, 044020 (2001), arXiv:hep-th/0007172

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  45. [45]

    Vacuum polarization in two-dimensional static spacetimes and dimensional reduction

    R. Balbinot, A. Fabbri, P. Nicolini, and P. J. Sutton, Vac- uum polarization in two-dimensional static space-times and dimensional reduction, Phys. Rev. D66, 024014 (2002), arXiv:hep-th/0202036

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  46. [46]

    IR Renormalisation of General Effective Actions and Hawking Flux in 2D Gravity Theories

    D. Hofmann and W. Kummer, IR renormalisation of gen- eral effective actions and Hawking flux in 2-D gravity theo- ries, Eur. Phys. J. C48, 291 (2006), arXiv:gr-qc/0512163

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  47. [47]

    Wu and J

    C.-H. Wu and J. Xu, Islands in non-minimal dilaton grav- ity: exploring effective theories for black hole evaporation, JHEP10, 094, arXiv:2303.03410 [hep-th]

    work page arXiv

  48. [48]

    R. M. Wald, The Back Reaction Effect in Particle Cre- ation in Curved Space-Time, Commun. Math. Phys.54, 1 (1977)

    work page 1977

  49. [49]

    R. M. Wald, Trace anomaly of a conformally invariant quantum field in curved spacetime, Phys. Rev. D17, 1477 (1978)

    work page 1978

  50. [50]

    R. M. Wald, Axiomatic Renormalization of the Stress Tensor of a Conformally Invariant Field in Conformally Flat Space-Times, Annals Phys.110, 472 (1978)

    work page 1978

  51. [51]

    Garfinkle, An Exact solution for 2+1 dimensional critical collapse, Phys

    D. Garfinkle, An Exact solution for 2+1 dimensional critical collapse, Phys. Rev. D63, 044007 (2001), arXiv:gr- qc/0008023. 7

    work page arXiv 2001

  52. [52]

    M. D. Roberts, Scalar Field Counterexamples to the Cosmic Censorship Hypothesis, Gen. Rel. Grav.21, 907 (1989)

    work page 1989

  53. [53]

    P. R. Brady, Analytic example of critical behaviour in scalar field collapse, Class. Quant. Grav.11, 1255 (1994)

    work page 1994

  54. [54]

    Critical Behavior of Black Hole Formation in a Scalar Wave Collapse

    Y. Oshiro, K. Nakamura, and A. Tomimatsu, Critical behavior of black hole formation in a scalar wave collapse, Prog. Theor. Phys.91, 1265 (1994), arXiv:gr-qc/9402017

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  55. [55]

    Perturbations of an exact solution for 2+1 dimensional critical collapse

    D. Garfinkle and C. Gundlach, Perturbations of an exact solution for (2+1)-dimensional critical collapse, Phys. Rev. D66, 044015 (2002), arXiv:gr-qc/0205107

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  56. [56]

    Scalar field critical collapse in 2+1 dimensions

    J. Ja lmu˙ zna, C. Gundlach, and T. Chmaj, Scalar field critical collapse in 2+1 dimensions, Phys. Rev. D92, 124044 (2015), arXiv:1510.02592 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  57. [57]

    P. R. Brady, Self-similar scalar field collapse: Naked sin- gularities and critical behavior, Phys. Rev. D51, 4168 (1995), arXiv:gr-qc/9409035

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  58. [58]

    A. V. Frolov, Perturbations and critical behavior in the self-similar gravitational collapse of a massless scalar field, Phys. Rev. D56, 6433 (1997), arXiv:gr-qc/9704040

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  59. [59]

    A. V. Frolov, Critical collapse beyond spherical symmetry: General perturbations of the Roberts solution, Phys. Rev. D59, 104011 (1999), arXiv:gr-qc/9811001

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  60. [60]

    A. V. Frolov, Continuous self-similarity breaking in criti- cal collapse, Phys. Rev. D61, 084006 (2000), arXiv:gr- qc/9908046

    work page arXiv 2000

  61. [61]

    Hawking, Gravitational radiation in an expanding uni- verse, J

    S. Hawking, Gravitational radiation in an expanding uni- verse, J. Math. Phys.9, 598 (1968)

    work page 1968

  62. [62]

    S. A. Hayward, Quasilocal gravitational energy, Phys. Rev. D49, 831 (1994), arXiv:gr-qc/9303030

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  63. [63]

    C. W. Misner and D. H. Sharp, Relativistic equations for adiabatic, spherically symmetric gravitational collapse, Phys. Rev.136, B571 (1964)

    work page 1964

  64. [64]

    W. C. Hernandez and C. W. Misner, Observer Time as a Coordinate in Relativistic Spherical Hydrodynamics, Astrophys. J.143, 452 (1966)

    work page 1966

  65. [65]

    P. R. Brady, C. M. Chambers, and S. M. C. V. Goncalves, Phases of massive scalar field collapse, Phys. Rev. D56, R6057 (1997), arXiv:gr-qc/9709014

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  66. [66]

    M. W. Choptuik, T. Chmaj, and P. Bizon, Critical behav- ior in gravitational collapse of a Yang-Mills field, Phys. Rev. Lett.77, 424 (1996), arXiv:gr-qc/9603051

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  67. [67]

    S. H. Hawley and M. W. Choptuik, Boson stars driven to the brink of black hole formation, Phys. Rev. D62, 104024 (2000), arXiv:gr-qc/0007039

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  68. [68]

    Bartnik and J

    R. Bartnik and J. Mckinnon, Particle - Like Solutions of the Einstein Yang-Mills Equations, Phys. Rev. Lett.61, 141 (1988)

    work page 1988

  69. [69]

    Semiclassical zero-temperature corrections to Schwarzschild spacetime and holography

    A. Fabbri, S. Farese, J. Navarro-Salas, G. J. Olmo, and H. Sanchis-Alepuz, Semiclassical zero-temperature correc- tions to Schwarzschild spacetime and holography, Phys. Rev. D73, 104023 (2006), arXiv:hep-th/0512167

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  70. [70]

    Static quantum corrections to the Schwarzschild spacetime

    A. Fabbri, S. Farese, J. Navarro-Salas, G. J. Olmo, and H. Sanchis-Alepuz, Static quantum corrections to the Schwarzschild spacetime, J. Phys. Conf. Ser.33, 457 (2006), arXiv:hep-th/0512179

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  71. [71]

    Static Black Holes With Back Reaction From Vacuum Energy

    P.-M. Ho and Y. Matsuo, Static Black Holes With Back Reaction From Vacuum Energy, Class. Quant. Grav.35, 065012 (2018), arXiv:1703.08662 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  72. [72]

    Static Black Hole and Vacuum Energy: Thin Shell and Incompressible Fluid

    P.-M. Ho and Y. Matsuo, Static Black Hole and Vacuum Energy: Thin Shell and Incompressible Fluid, JHEP03, 096, arXiv:1710.10390 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  73. [73]

    P.-M. Ho, H. Kawai, Y. Matsuo, and Y. Yokokura, Back Reaction of 4D Conformal Fields on Static Geometry, JHEP11, 056, arXiv:1807.11352 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  74. [74]

    P.-M. Ho, Y. Matsuo, and Y. Yokokura, Analytic descrip- tion of semiclassical black-hole geometry, Phys. Rev. D 102, 024090 (2020), arXiv:1912.12855 [hep-th]

    work page arXiv 2020

  75. [75]

    Barcel´ o, V

    C. Barcel´ o, V. Boyanov, R. Carballo-Rubio, and L. J. Garay, Semiclassical gravity effects near hori- zon formation, Class. Quant. Grav.36, 165004 (2019), arXiv:1904.06558 [gr-qc]

    work page arXiv 2019

  76. [76]

    Arrechea, C

    J. Arrechea, C. Barcel´ o, R. Carballo-Rubio, and L. J. Garay, Schwarzschild geometry counterpart in semi- classical gravity, Phys. Rev. D101, 064059 (2020), arXiv:1911.03213 [gr-qc]

    work page arXiv 2020

  77. [77]

    Beltr´ an-Palau, A

    P. Beltr´ an-Palau, A. del R´ ıo, and J. Navarro-Salas, Quan- tum corrections to the Schwarzschild metric from vac- uum polarization, Phys. Rev. D107, 085023 (2023), arXiv:2212.08089 [gr-qc]

    work page arXiv 2023

  78. [78]

    Arrechea, C

    J. Arrechea, C. Breen, A. Ottewill, L. Pisani, and P. Tay- lor, Renormalized stress-energy tensor for scalar fields in the Boulware state with applications to extremal black holes, Phys. Rev. D111, 085009 (2025), arXiv:2409.04528 [gr-qc]

    work page arXiv 2025

  79. [79]

    Numajiri, K

    K. Numajiri, K. Okabayashi, and S. Mukohyama, Boul- ware vacuum vs regularity: Thoughts on anomaly- induced effective action, Phys. Rev. D111, 085024 (2025), arXiv:2411.12617 [gr-qc]

    work page arXiv 2025

  80. [80]

    C. R. Evans and J. S. Coleman, Observation of critical phenomena and self-similarity in the gravitational col- lapse of radiation fluid, Phys. Rev. Lett.72, 1782 (1994), arXiv:gr-qc/9402041

    work page internal anchor Pith review Pith/arXiv arXiv 1994

Showing first 80 references.