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arxiv: 2604.27897 · v1 · submitted 2026-04-30 · 🌀 gr-qc · hep-th

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Probing mass inflation in polymerized vacuum regular black holes via colliding null shells

Hongguang Liu , Ioannis Soranidis
Authors on Pith no claims yet

Pith reviewed 2026-05-07 07:53 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords regular black holesmass inflationpolymerized vacuumnull shellsinner horizondegenerate horizonminimal length scaleBirkhoff theorem
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The pith

Inner-extremal regular black holes with degenerate inner horizons exist only for a tuned mass in polymerized vacuum.

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

The paper derives a class of inner-extremal regular black hole solutions in polymerized vacuum that feature a degenerate inner horizon. These solutions are unique within the framework due to a Birkhoff-type theorem and occur only when the mass takes a specific value fixed by the theory parameters. The authors then use a setup of colliding null shells to study mass inflation near the inner horizon in both these degenerate cases and the corresponding non-degenerate regular black holes. They identify when mass inflation is significant and how a minimal length scale modifies this process. The analysis also addresses the stability of these black hole configurations against such perturbations.

Core claim

A class of inner-extremal regular black hole solutions with degenerate inner horizons arises in polymerized vacuum configurations that admit a Birkhoff-type theorem, rendering them unique, and such configurations exist only for a finely tuned mass value. Building on this and non-degenerate solutions, a generic analysis of mass inflation in four-dimensional spacetimes via colliding null shells reveals conditions for its significance and the role of the minimal length scale, with comments on stability under these perturbations.

What carries the argument

Polymerized vacuum configurations admitting a Birkhoff-type theorem that yield unique inner-extremal regular black holes with degenerate horizons at tuned mass, analyzed through colliding null-shell perturbations to probe mass inflation.

Load-bearing premise

The polymerized vacuum configurations constitute valid effective quantum-gravity solutions that admit a Birkhoff-type theorem rendering the geometries unique within the framework.

What would settle it

A numerical simulation of null shell collisions in the polymerized vacuum geometry that fails to show the predicted mass inflation dependence on the minimal length scale for the tuned mass case.

Figures

Figures reproduced from arXiv: 2604.27897 by Hongguang Liu, Ioannis Soranidis.

Figure 1
Figure 1. Figure 1: FIG. 1 view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 view at source ↗
read the original abstract

We derive a class of inner-extremal regular black hole solutions characterized by a degenerate inner horizon. These geometries arise as polymerized vacuum configurations inspired by loop quantum gravity and constitute effective quantum-gravity solutions that admit a Birkhoff-type theorem, rendering them unique within the considered framework. We show that such inner-extremal horizon configurations exist only for a finely tuned value of the mass determined by the parameters of the theory. Building on this construction, together with the corresponding non-degenerate regular black hole solutions, we perform a generic analysis of the mass inflation phenomenon in four-dimensional spacetimes using a colliding null-shell setup near the inner horizon. We identify the conditions under which mass inflation becomes significant and examine how the presence of a minimal length scale affects this behavior, with particular emphasis on the case where such a scale is motivated by loop quantum gravity. Finally, we comment on the stability of these configurations under the null-shell perturbations considered in our analysis.

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 / 3 minor

Summary. The paper derives a class of inner-extremal regular black hole solutions characterized by a degenerate inner horizon. These arise as polymerized vacuum configurations in an LQG-inspired effective theory and are claimed to be unique within the framework by virtue of a Birkhoff-type theorem. Such configurations exist only for a finely tuned value of the mass fixed by the theory parameters. Using these backgrounds together with the corresponding non-degenerate regular black holes, the authors perform a generic analysis of mass inflation via colliding null shells near the inner horizon, identify conditions for significant inflation, examine the role of the minimal length scale, and comment on stability under the perturbations.

Significance. If the uniqueness claim and the mass-inflation analysis hold, the work provides a concrete effective-theory probe of how a minimal length scale modifies classical mass-inflation behavior in regular black holes. The colliding-null-shell setup is a standard, generic tool that allows direct comparison with the Reissner–Nordström case and could yield falsifiable signatures of polymerization. The explicit construction of inner-extremal solutions also supplies a controlled arena for studying horizon stability in quantum-gravity-inspired models.

major comments (2)
  1. [§3] §3 (Birkhoff-type theorem for polymerized vacuum): The central claim that inner-extremal geometries are unique and exist only for a tuned mass rests on the assertion that the polymerized effective equations admit a Birkhoff-type theorem. Polymerization replaces curvature scalars with holonomy functions of the minimal length ℓ, yielding modified vacuum equations that are no longer the Einstein equations. The manuscript must explicitly integrate the modified constraints or demonstrate that the effective constraint algebra closes with only a single integration constant; the classical Birkhoff proof does not automatically extend. Without this verification the tuning requirement is not forced by the dynamics and the subsequent mass-inflation analysis, which treats the reported family as the complete set of backgrounds, loses its generality.
  2. [§4] §4 (inner-extremal solutions and mass tuning): The statement that degenerate-horizon solutions exist only for a finely tuned mass must be supported by the explicit degeneracy condition (e.g., the vanishing of the metric function and its derivative at the inner horizon, or equality of surface gravities). The paper should display the algebraic relation between the mass parameter and the polymerization scale ℓ that enforces this condition and confirm it is not an additional assumption. This relation is load-bearing for the claim that tuning is “determined by the parameters of the theory.”
minor comments (3)
  1. [Abstract] The abstract summarizes the results but contains no equations or explicit tuning relation; adding a one-line statement of the mass-tuning condition would improve clarity for readers.
  2. [Notation] Notation for the polymerization function and the minimal length scale should be introduced once and used uniformly in all sections and figures.
  3. [Introduction] A short paragraph comparing the present null-shell setup with earlier mass-inflation analyses in regular black holes (e.g., those using the Ori or Poisson-Israel models) would help situate the new results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments, which help clarify the presentation of the Birkhoff-type theorem and the mass-tuning condition. We address each major comment in turn and will revise the manuscript to incorporate the requested explicit derivations.

read point-by-point responses

  1. Referee: [§3] §3 (Birkhoff-type theorem for polymerized vacuum): The central claim that inner-extremal geometries are unique and exist only for a tuned mass rests on the assertion that the polymerized effective equations admit a Birkhoff-type theorem. Polymerization replaces curvature scalars with holonomy functions of the minimal length ℓ, yielding modified vacuum equations that are no longer the Einstein equations. The manuscript must explicitly integrate the modified constraints or demonstrate that the effective constraint algebra closes with only a single integration constant; the classical Birkhoff proof does not automatically extend. Without this verification the tuning requirement is not forced by the dynamics and the subsequent mass-inflation analysis, which treats the reported family as the complete set of backgrounds, loses its generality.

    Authors: We agree that an explicit integration of the modified constraints is necessary to rigorously establish the Birkhoff-type theorem in the polymerized effective theory. In the revised version we will add a dedicated subsection (or appendix) to §3 that starts from the polymerized vacuum equations, integrates the modified Hamiltonian and diffeomorphism constraints step by step, and demonstrates that the effective constraint algebra closes with precisely one integration constant—the mass parameter. This derivation will confirm that the inner-extremal solutions form the complete set of static, spherically symmetric vacuum configurations for given ℓ, thereby justifying that the mass tuning arises directly from the dynamics rather than from an external assumption. The mass-inflation analysis will then be framed as applying to this unique family. revision: yes

  2. Referee: [§4] §4 (inner-extremal solutions and mass tuning): The statement that degenerate-horizon solutions exist only for a finely tuned mass must be supported by the explicit degeneracy condition (e.g., the vanishing of the metric function and its derivative at the inner horizon, or equality of surface gravities). The paper should display the algebraic relation between the mass parameter and the polymerization scale ℓ that enforces this condition and confirm it is not an additional assumption. This relation is load-bearing for the claim that tuning is “determined by the parameters of the theory.”

    Authors: We acknowledge that the explicit degeneracy conditions and the resulting algebraic relation were not displayed with sufficient detail. In the revision we will insert the full calculation in §4: we impose f(r_in) = 0 and f'(r_in) = 0 (equivalently, vanishing surface gravity) on the polymerized metric function, solve the resulting algebraic system, and obtain the explicit relation M = M(ℓ, β) that fixes the mass in terms of the polymerization scale ℓ and the other theory parameters. We will also show that this relation is required by the effective field equations once the inner horizon is required to be degenerate, confirming it is not an extra assumption. The same section will include a brief verification that the non-degenerate family remains available for generic masses, allowing direct comparison in the mass-inflation analysis. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of inner-extremal polymerized solutions

full rationale

The paper derives a class of inner-extremal regular black hole solutions from polymerized vacuum configurations and demonstrates that degenerate inner horizons occur only for a specific mass value fixed by the theory parameters. This condition is presented as a derived result from the effective equations rather than a parameter chosen by hand and relabeled as a prediction. The invocation of a Birkhoff-type theorem to assert uniqueness within the framework does not reduce the central claims to self-definition or tautology, as the subsequent colliding null-shell analysis of mass inflation constitutes independent content performed on the constructed backgrounds. No equations are shown to be equivalent by construction, and no load-bearing step relies solely on an unverified self-citation that collapses the result to its inputs. The derivation chain remains self-contained against the stated effective model.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claims rest on the validity of polymerized vacuum as an effective LQG description and on the applicability of a Birkhoff-type theorem in that framework; the tuned mass is introduced to achieve degeneracy.

free parameters (1)
  • mass tuning parameter
    Mass must be finely tuned to the theory parameters for the inner horizon to become degenerate.
axioms (2)
  • domain assumption Birkhoff-type theorem holds for polymerized vacuum configurations
    Invoked to establish uniqueness of the derived geometries.
  • domain assumption Polymerized vacuum provides valid effective quantum-gravity solutions
    Basis for the regular black hole construction inspired by loop quantum gravity.
invented entities (1)
  • inner-extremal polymerized regular black holes no independent evidence
    purpose: Singularity-free black hole geometries with degenerate inner horizon
    New class derived in the paper; no independent evidence supplied.

pith-pipeline@v0.9.0 · 5463 in / 1584 out tokens · 54382 ms · 2026-05-07T07:53:54.765386+00:00 · methodology

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Reference graph

Works this paper leans on

85 extracted references · 7 canonical work pages · 1 internal anchor

  1. [1]

    [69], owing to the structural similarity between the metric function in quasitopological gravity and the one obtained in our formulation

    Fine-tuning of the mass parameter The proof of the finely tuned mass follows closely the strat- egy of Ref. [69], owing to the structural similarity between the metric function in quasitopological gravity and the one obtained in our formulation. We assume the existence of a degenerate inner horizon located at some radiusr ∗. For con- venience, we introduc...

  2. [2]

    (7), one observes that the parameterr 0 coincides with the minimal length scale ℓ

    Non-degenerate inner horizon For the Hayward model described by Eq. (7), one observes that the parameterr 0 coincides with the minimal length scale ℓ. This follows by taking the large-mass limit of the inner- horizon radius given in Eq. (10), which precisely yields the definition ofr 0 introduced in Eq. (32). In this model, there- fore, we haver 0 =ℓ. We ...

  3. [3]

    Degenerate inner horizon We now turn to the inner-extremal solution constructed in Sec. II B. This case has to be treated separately from the Hay- ward example. In the Hayward geometry the regularization scale is fixed and the mass parameter can be varied contin- uously, so the neighboring DHBI regions are naturally de- scribed by the same family of metri...

  4. [4]

    S. W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D14, 2460 (1976)

    1976

  5. [5]

    Cardoso and P

    V . Cardoso and P. Pani, Testing the nature of dark compact ob- 15 jects: a status report, Living Rev. Relativ.22, 4 (2019)

    2019

  6. [6]

    Barack, V

    L. Barack, V . Cardoso, S. Nissanke, and T. P. Sotiriou (eds.), Black holes, gravitational waves and fundamental physics: a roadmap, Class. Quantum Gravity36, 143001 (2019)

    2019

  7. [7]

    Murk, Nomen non est omen: Why it is too soon to identify ultra-compact objects as black holes, Int

    S. Murk, Nomen non est omen: Why it is too soon to identify ultra-compact objects as black holes, Int. J. Mod. Phys. D32, 2342012 (2023)

    2023

  8. [8]

    J. M. Bardeen Non-singular general relativistic gravitational collapse,Proceedings of the International Conference GR5 (Tbilisi University Press, Tbilisi, 1968)

    1968

  9. [9]

    Dymnikova, Vacuum nonsingular black hole, Gen

    I. Dymnikova, Vacuum nonsingular black hole, Gen. Relativ. Gravit.24, 235 (1992)

    1992

  10. [10]

    S. A. Hayward, Formation and Evaporation of Nonsingular Black Holes, Phys. Rev. Lett.96, 031103 (2006)

    2006

  11. [11]

    P. O. Mazur and E. Mottola, Gravitational vacuum condensate stars, Proc. Natl. Acad. Sci.101, 9545 (2004)

    2004

  12. [12]

    P. O. Mazur and E. Mottola, Gravitational Condensate Stars: An Alternative to Black Holes, Universe9, 88 (2023)

    2023

  13. [13]

    H. G. Ellis, Ether flow through a drainhole: A particle model in general relativity, J. Math. Phys.14, 104 (1973)

    1973

  14. [14]

    M. S. Morris and K. S. Thorne, Wormholes in spacetime and their use for interstellar travel: A tool for teaching general rela- tivity, Am. J. Phys.56, 395 (1988)

    1988

  15. [15]

    Simpson and M

    A. Simpson and M. Visser, Black-bounce to traversable worm- hole, J. Cosmol. Astropart. Phys. 02 (2019) 042

    2019

  16. [16]

    Lunin and S

    O. Lunin and S. D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B623, 342, (2002)

    2002

  17. [17]

    S. D. Mathur, The fuzzball proposal for black holes: an elemen- tary review, Fortsch. Phys.53, 793 (2005)

    2005

  18. [18]

    Poisson and W

    E. Poisson and W. Israel, Inner-horizon instability and mass in- flation in black holes, Phys. Rev. Lett.63, 1663 (1989)

    1989

  19. [19]

    Poisson and W

    E. Poisson and W. Israel, Internal structure of black holes, Phys. Rev. D41, 1796 (1990)

    1990

  20. [20]

    P. R. Brady and J. D. Smith, Black Hole Singularities: A Nu- merical Approach, Phys. Rev. Lett.75, 1256 (1995)

    1995

  21. [21]

    A. J. S. Hamilton and P. P. Avelino, The physics of the rela- tivistic counter-streaming instability that drives mass inflation inside black holes, Phys. Rept.495, 1 (2010)

    2010

  22. [22]

    Hwang and D.-h

    D.-i. Hwang and D.-h. Yeom, Internal structure of charged black holes, Phys. Rev. D84, 064020 (2011)

    2011

  23. [23]

    Carballo-Rubio, F

    R. Carballo-Rubio, F. Di Filippo, S. Liberati, and M. Visser, Mass Inflation without Cauchy Horizons, Phys. Rev. Lett.133, 181402 (2024)

    2024

  24. [24]

    V . P. Frolov and A. Zelnikov, Regular Black Holes in Qua- sitopological Gravity: Null Shells and Mass Inflation, arXiv: 2601.01861 [gr-qc] (2026)

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  25. [25]

    V . P. Frolov and A. Zelnikov, Quantum radiation from an evapo- rating nonsingular black hole, Phys. Rev. D 95, 124028 (2017)

    2017

  26. [26]

    E. G. Brown, R. B. Mann, and L. Modesto, Mass inflation in the loop black hole, Phys. Rev. D84, 104041 (2011)

    2011

  27. [27]

    Bonanno A.-P

    A. Bonanno A.-P. Khosravi, and F. Saueressig, Regular black holes with stable cores, Phys. Rev. D103, 124027 (2021)

    2021

  28. [28]

    Husain, J

    V . Husain, J. G. Kelly, R. Santacruz, and E. Wilson-Ewing, Quantum gravity of dust collapse: shock waves from black holes, Phys. Rev. Lett.128, 121301 (2022)

    2022

  29. [29]

    Carballo-Rubio, F

    R. Carballo-Rubio, F. Di Filippo, S. Liberati, C. Pacilio, and M. Visser, On the Inner Horizon Instability of Non-Singular Black Holes, Universe2022, 8(4), 204 (2022)

    2022

  30. [30]

    Rinaldi, L

    M.l Bertipagani, M. Rinaldi, L. Sebastiani, and S. Zerbini, Non- singular black holes and mass inflation in modified gravity, Physics of the Dark Universe33, 100853 (2021)

    2021

  31. [31]

    Bonanno and F

    A. Bonanno and F. Saueressig, Stability properties of Regular Black Holes, arXiv: 2211.09192 [gr-qc] (2022)

    work page arXiv 2022

  32. [32]

    Bambi (ed.),Regular Black Holes: Towards a New Paradigm of Gravitational Collapse(Springer Singapore, 2023)

    C. Bambi (ed.),Regular Black Holes: Towards a New Paradigm of Gravitational Collapse(Springer Singapore, 2023)

    2023

  33. [33]

    Barcel ´o, V

    C. Barcel ´o, V . Boyanov, R. Carballo-Rubio, and L. J. Garay, Classical mass inflation versus semiclassical inner horizon in- flation, Phys. Rev. D106, 124006 (2022)

    2022

  34. [34]

    McMaken, Semiclassical instability of inner-extremal regu- lar black holes, Phys

    T. McMaken, Semiclassical instability of inner-extremal regu- lar black holes, Phys. Rev. D107, 125023 (2023)

    2023

  35. [35]

    Cauchy Horizon (In)Stability of Regular Black Holes

    A. Bonanno, A. Panassiti, and F. Saueressig, Cauchy Horizon (In)Stability of Regular Black Holes, arXiv: 2507.03581 [gr- qc] (2025)

    work page arXiv 2025

  36. [36]

    Cao, L.-Y

    L.-M. Cao, L.-Y . Li, L.-B. Wu, and Y .-S. Zhou, The instability of the inner horizon of the quantum-corrected black hole, Eur. Phys. J. C84, 507 (2024)

    2024

  37. [37]

    Carballo-Rubio, F

    R. Carballo-Rubio, F. Di Filippo, S. Liberati, C. Pacilio, and M. Visser, Regular black holes without mass inflation instability, J. High Energ. Phys.2022, 118 (2022)

    2022

  38. [38]

    Pellicer and R

    R. Pellicer and R. J. Torrence, Nonlinear Electrodynamics and General Relativity, J. Math. Phys.10, 1718 (1969)

    1969

  39. [39]

    K. A. Bronnikov, V . N. Melnikov, G. N. Shikin, and K. P. Sta- niukovich, Scalar, electromagnetic, and gravitational fields in- teraction: Particlelike solutions, Ann. Phys.118, 84 (1979)

    1979

  40. [40]

    Ay ´on-Beato and E

    E. Ay ´on-Beato and E. Garc ´ıa, Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics, Phys. Rev. Lett.80, 5056 (1998)

    1998

  41. [41]

    Ay ´on-Beato and E

    E. Ay ´on-Beato and E. Garc ´ıa, Non-Singular Charged Black Hole Solution for Non-Linear Source, Gen. Relativ. Gravit.31, 629 (1999)

    1999

  42. [42]

    Ay ´on-Beato and E

    E. Ay ´on-Beato and E. Garc´ıa, New regular black hole solution from nonlinear electrodynamics, Phys. Lett. B464, 25 (1999)

    1999

  43. [43]

    Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics

    K. A. Bronnikov, Comment on “Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics”, Phys. Rev. Lett.85, 4641 (2000)

    2000

  44. [44]

    K. A. Bronnikov, Regular magnetic black holes and monopoles from nonlinear electrodynamics, Phys. Rev. D63, 044005 (2001)

    2001

  45. [45]

    Burinskii and S

    A. Burinskii and S. R. Hildebrandt, New type of regular black holes and particlelike solutions from nonlinear electrodynam- ics, Phys. Rev. D65, 104017 (2002)

    2002

  46. [46]

    Dymnikova, Regular electrically charged vacuum structures with de Sitter centre in nonlinear electrodynamics coupled to general relativity, Class

    I. Dymnikova, Regular electrically charged vacuum structures with de Sitter centre in nonlinear electrodynamics coupled to general relativity, Class. Quantum Gravity21, 4417 (2004)

    2004

  47. [47]

    Balart and E

    L. Balart and E. C. Vagenas, Regular black holes with a nonlin- ear electrodynamics source, Phys. Rev. D90, 124045 (2014)

    2014

  48. [48]

    Fan and X

    Z.-Y . Fan and X. Wang, Construction of regular black holes in general relativity, Phys. Rev. D94, 124027 (2016)

    2016

  49. [49]

    Construction of regular black holes in general relativity

    K. A. Bronnikov, Comment on “Construction of regular black holes in general relativity”, Phys. Rev. D96, 128501 (2017)

    2017

  50. [50]

    Construction of regular black holes in general relativity

    B. Toshmatov, Z. Stuchl ´ık, and B. Ahmedov, Comment on “Construction of regular black holes in general relativity”, Phys. Rev. D98, 028501 (2018)

    2018

  51. [51]

    K. A. Bronnikov, Regular Black Holes Sourced by Nonlinear Electrodynamics, in C. Bambi (ed.) Regular Black Holes: To- wards a New Paradigm of Gravitational Collapse (Springer Sin- gapore, 2023)

    2023

  52. [52]

    Bueno, P

    P. Bueno, P. A. Cano, and R. A. Hennigar, Regular black holes from pure gravity, Phys. Lett. B861, 139 (2025)

    2025

  53. [53]

    Bueno, P

    P. Bueno, P. A. Cano, R. A. Hennigar, and ´A. J. Murcia Regular black holes from thin-shell collapse, Phys. Rev. D111, 104009 (2025)

    2025

  54. [54]

    Bueno, P

    P. Bueno, P. A. Cano, R. A. Hennigar, and ´A. J. Murcia Dy- namical Formation of Regular Black Holes, Phys. Rev. Lett. 134, 181401 (2025)

    2025

  55. [55]

    Bueno, P

    P. Bueno, P. A. Cano, R. A. Hennigar, ´A. J. Murcia, and A. Vincente-Cano, Regular black holes from Oppenheimer-Snyder collapse, Phys. Rev. D112, 064039 (2025). 16

    2025

  56. [56]

    R. A. Hennigar, D. Kubiz ˇn´ak, S. Murk, and I. Soranidis, Ther- modynamics of regular black holes in anti-de Sitter space, J. High Energ. Phys. 2025, 121 (2025)

    2025

  57. [57]

    V . P. Frolov, A. Koek, J. P. Soto, and A. Zelnikov, Regular black holes inspired by quasitopological gravity, Phys. Rev. D111, 044034 (2025)

    2025

  58. [58]

    P. G. S. Fernandes, Singularity resolution and inflation from an infinite tower of regularized curvature corrections, Phys. Rev. D112, 084028 (2025)

    2025

  59. [59]

    Borissova and R

    J. Borissova and R. Carballo-Rubio, Regular black holes from pure gravity in four dimensions, arXiv: 2602.16773 [gr-qc] (2026)

    work page arXiv 2026

  60. [60]

    Bueno, P

    P. Bueno, P. A. Cano, R. A. Hennigar, and ´A. J. Murcia, Reg- ular black hole formation in four-dimensional nonpolynomial gravities, Phys. Rev. D113, 024019 (2026)

    2026

  61. [61]

    Giesel, H

    K. Giesel, H. Liu, E. Rullit, P. Singh, and S. A. Weigl, Em- bedding generalized Lema ˆıtre-Tolman-Bondi models in poly- merized spherically symmetric spacetimes, Phys. Rev. D110, 104017 (2025)

    2025

  62. [62]

    K.Giesel, H. Liu, P. Singh, and S. A. Weigl, Regular black holes and their relationship to polymerized models and mimetic grav- ity, Phys. Rev. D111, 064064 (2025)

    2025

  63. [63]

    Giesel and H

    K. Giesel and H. Liu, From Principles to Effective Models: A Constructive Framework for Effective Covariant Actions with a Unique Vacuum Solution, arXiv: 2512.24960 (2025)

    work page arXiv 2025

  64. [64]

    Han and H

    M. Han and H. Liu, Covariantµ¯-scheme effective dynam- ics, mimetic gravity, and nonsingular black holes: Applications to spherically symmetric quantum gravity, Phys. Rev. D109, 084033 (2024)

    2024

  65. [65]

    Han and H

    M. Han and H. Liu, Improved effective dynamics of loop- quantum-gravity black hole and Nariai limit, Classical Quan- tum Gravity39, 035011 (2022)

    2022

  66. [66]

    Ben Achour, F

    J. Ben Achour, F. Lamy, H. Liu and K. Noui, Non-singular black holes and the Limiting Curvature Mechanism: A Hamil- tonian perspective, JCAP05(2018), 072 J. Cosmol. Astropart. Phys.05, 072 (2018)

    2018

  67. [67]

    Ben Achour, F

    J. Ben Achour, F. Lamy, H. Liu, and K. Noui, Polymer Schwarzschild black hole: An effective metric, Europhysics let- ters123, 20006 (2018)

    2018

  68. [68]

    Bueno, P

    P. Bueno, P. A. Cano, and R. A. Hennigar, (Generalized) quasi- topological gravities at all orders Classical Quantum Gravity 37, 015002 (2019)

    2019

  69. [69]

    Bueno, P

    P. Bueno, P. A. Cano, R. A. Hennigar, M. Lu, and J. Moreno, Generalized quasi-topological gravities: the whole shebang, Classical Quantum Gravity40, 015004 (2022)

    2022

  70. [70]

    Moreno and ´A

    J. Moreno and ´A. J. Murcia, Classification of generalized qua- sitopological gravities, Phys. Rev. D108, 044016 (2023)

    2023

  71. [71]

    Bueno, R

    P. Bueno, R. A. Hennigar, and ´A. J. Murcia, Birkhoff implies Quasi-topological, arXiv: 2510.25823 (2025)

    work page arXiv 2025

  72. [72]

    Di Filippo, I

    F. Di Filippo, I. Kol ´aˇr, and D. Kubiz ˇn´ak, Inner-extremal regu- lar black holes from pure gravity, Phys. Rev. D111, L041505 (2025)

    2025

  73. [73]

    Lasky, A

    P. Lasky, A. Lun, and R. Burston, Initial value formalism for dust collapse, arXiv: gr-qc/0606003 (2007)

    work page arXiv 2007

  74. [74]

    Liu and I

    H. Liu and I. Soranidis, Regular ultracompact objects with anti- de Sitter cores as polymerized vacuum solutions, (to appear)

  75. [75]

    Takahashi and T

    K. Takahashi and T. Kobayashi, Extended mimetic gravity: Hamiltonian analysis and gradient instabilities, J. Cosmol. As- tropart. Phys.11, 038 (2017)

    2017

  76. [76]

    Langlois, M

    D. Langlois, M. Mancarella, K. Noui and F. Vernizzi, Mimetic gravity as DHOST theories, J. Cosmol. Astropart. Phys.02, 036 (2019)

    2019

  77. [77]

    Arrechea, S

    J. Arrechea, S. Liberati, H. Neshat, and V . Vellucci, From de Sitter to anti–de Sitter singularity regularization: Theory and phenomenology, Phys. Rev. D112, 124029 (2025)

    2025

  78. [78]

    Murk and I

    S. Murk and I. Soranidis, Kinematic and energy properties of dynamical regular black holes, Phys. Rev. D108, 124007 (2023)

    2023

  79. [79]

    Dray and G

    T. Dray and G. ’t Hooft, The effect of spherical shells of matter on the Schwarzschild black hole, Commun. Math. Phys.99, 613 (1985)

    1985

  80. [80]

    Barrab `es and W

    C. Barrab `es and W. Israel, Thin shells in general relativity and cosmology: The lightlike limit, Phys. Rev. D43, 1129 (1991)

    1991

Showing first 80 references.