Pith. sign in

REVIEW 3 major objections 6 minor 50 references

Dust shell in effective loop quantum black hole model

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read An effective loop quantum black hole model with a thin dust shell is claimed to produce a bounce, a spacelike shell trajectory crossing the outer horizon for masses above about 0.39 ζ, and a black hole horizon with finite lifetime.

desk verdict Solid reduced-action derivation, but the discontinuity claims ride on a junction condition that is imposed, not derived. read the letter →

arxiv 2506.04589 v3 pith:RTCUGSY2 submitted 2025-06-05 gr-qc

Hanno Sahlmann , Cong Zhang This is my paper
classification gr-qc MSC 83C5783C4583C75
keywords dustshelleffectiveloopquantumblackholereducedactionjunctionconditionsbouncehorizonlifetimesphericallysymmetricgravityspaceliketrajectory
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper constructs an action principle for a thin dust shell in an effective spherically symmetric loop quantum black hole model, restoring the diffeomorphism constraint and gauge-fixing terms that earlier treatments solve away. Substituting vacuum geometries on the two sides of the shell reduces the action to a single dynamical variable, the shell radius $x$, and the paper derives the shell's equation of motion from that reduced action. The central claim is that the shell bounces instead of collapsing to a singularity, and that for shell masses above roughly $0.39\,\zeta$ the bounce lies inside the trapped region: the trajectory becomes spacelike, crosses the outer horizon, and the black hole horizon has a finite lifetime (about $12.158\,\zeta$ for $M_+=4\zeta$). The paper also claims that the metric is not continuous across the shell; instead the shell's proper time is continuous, and the exterior and interior time coordinates differ. If correct, these results give concrete, quantitative predictions for how quantum gravity corrections could resolve the endpoint of dust collapse.

What carries the argument

The key object is the reduced action $S=\int(\dot{x}\Pi-M_+-M_-)\,dt$, obtained by substituting the vacuum effective solutions on both sides of the shell into the total action and eliminating all fields except the shell radius $x$ and the exterior mass $M_+$. The momentum $\Pi$ in this action is built from elliptic integrals of the first kind (Eq. (34)), with the shell momentum $p$ determined by the junction condition (23), and the equation of motion (38) is obtained by varying this reduced action; integrating (38) together with (23) produces the bounce, the spacelike segment, and the finite horizon lifetime.

What would settle it

Recompute $N(x^-)$ and $N_x(x^-)$ from the evolution equations (40) using the alternative continuity condition (59) for the induced metric instead of (61); if a real lapse exists through the bounce, then the spacelike segment and finite horizon lifetime are artifacts of the imposed junction rule. A second check would be to solve the dust shell trajectory in a covariant extension that reproduces the same vacuum dynamics and see whether the trajectory remains timelike.

Watch

Extended reading notes

Core claim

The paper's central claim is that a dust shell in an effective loop quantum black hole spacetime can be treated consistently through a reduced action $S=\int(\dot{x}\Pi-M_+-M_-)\,dt$ whose only dynamical variables are the shell radius $x$ and the exterior mass $M_+$. Varying this action gives the evolution equation (38) for $x$, whose classical limit reproduces the standard dust-shell equation of motion. Numerical integration shows that the shell first collapses, then bounces; for $M_+=m\gtrsim 0.390\,\zeta$ with $M_-=0$, the bounce occurs inside the trapped region, the shell's worldline becomes spacelike as measured by the exterior metric, it crosses the outer horizon, and the horizon lifetime is finite, with $\Delta\tau\approx 12.158\,\zeta$ in the example $m=4\zeta$. To keep the lapse real at the bounce, the paper replaces continuity of the induced metric by continuity of the shell's proper time (Eq. (61)); this makes the metric discontinuous at the shell and makes the exterior and interior time coordinates differ, while the shell trajectory remains timelike according to the interior metric.

Load-bearing premise

The load-bearing premise is that the junction condition (61), which keeps the shell's proper time continuous rather than the metric, is the right rule; it is imposed to keep the lapse real at the bounce and is not derived from the action or from an independent physical principle.

Editorial extensions

If this is right

  • The dust shell bounces instead of collapsing to a singularity, so in this model black hole formation from dust collapse does not end at infinite density.
  • For $M_+=m\gtrsim 0.390\,\zeta$ with $M_-=0$, the bounce lies in the trapped region: the shell trajectory becomes spacelike, crosses the outer horizon, and the horizon has a finite proper lifetime (about $12.158\,\zeta$ for $m=4\zeta$).
  • The metric is discontinuous at the shell: the shell's proper time is continuous, but the exterior and interior time coordinates are not equal, contrary to the implicit coordinate continuity assumed in earlier shock-wave analyses.
  • In the limit $\zeta\to 0$, the shell equation of motion reduces to the classical dust-shell equation of motion, so the new predictions are pure quantum corrections.
  • The effective dust-shell Lagrangian is not the shell's proper time, indicating that matter coupling in the effective theory differs from classical matter coupling.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Whether the finite horizon lifetime is physical hangs on the junction rule (61), which is imposed to keep the lapse real rather than derived; if the correct rule instead preserves continuity of the induced metric, the spacelike segment and horizon lifetime may disappear.
  • The reduced-action method suggests a route to treating shell-crossing singularities in dust-ball collapse as a sequence of thin-shell junctions, provided discontinuities of the metric at each crossing are allowed.
  • A covariant completion of the effective model, of the kind the paper cites as future work, could settle whether the spacelike segment is genuine or an artifact of the non-covariant gauge fixing.
  • The sharp threshold $M_+\approx 0.390\,\zeta$ for the appearance of the spacelike segment is a quantitative prediction that can be compared with other effective black hole models or with full quantum evolution.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper reformulates an effective loop quantum black hole model as a constrained system with both Hamiltonian and diffeomorphism constraints plus gauge-fixing terms, couples a dust shell through an action, and reduces the dynamics to the shell radius x and the exterior mass M_+. The derived evolution equation (38) has the classical GR limit (39). Numerically, the shell can bounce instead of collapsing to a singularity, and for sufficiently large M_+ the trajectory develops a spacelike segment as measured by the exterior Painlevé-Gullstrand metric, crosses the outer horizon, and gives a finite horizon lifetime. The paper further argues that the metric is discontinuous across the shell and that the interior and exterior PG time coordinates differ, based on a modified junction condition (61).

Significance. The reduced-action derivation is a genuine technical advance: it bypasses weak-solution ambiguities, the classical limit (39) matches general relativity, no constants are fitted to data, and the numerical setup is explicit. If the junction condition (61) were derived from the action, the finite-horizon-lifetime and metric-discontinuity claims would be significant for effective LQG collapse models. As it stands, however, the central claims are conditional on an imposed matching rule, and the paper itself in Section VI acknowledges that the spacelike segment may be an artifact of the lack of covariance. The algebra leading to Eq. (38) is detailed and appears sound, but the load-bearing junction condition remains an assumption.

major comments (3)
  1. [Section V.B, Eq. (61)] The central new results — the discontinuity of the metric, the nonzero time-coordinate difference t and t_-, and the finite horizon lifetime — follow from replacing the standard induced-metric continuity condition (59) by the absolute-value condition (61), which is introduced to keep N(x-) real at the bounce. This condition is not derived from the action (12), from the Hamiltonian constraints, or from any junction principle. The manuscript itself states in Section VI that it is not yet known whether the spacelike segment is physical or merely an artifact of the model's lack of covariance. Because Eqs. (38) and (23) alone do not determine the matching rule, the headline claims are not established unless Eq. (61) is derived from the action or replaced by a physically motivated junction condition.
  2. [Section V.B, Eqs. (53)-(54), (62)] The reconstruction of N(x-) and N^x(x-) uses a piecewise solution with an interior point x0 where chi^2 vanishes, and the sign choice in Eq. (61) is needed to keep N(x-) real. No check is provided that the resulting distributional metric satisfies the effective equations of motion coming from the action (12) in the shell region; the junction conditions (19)-(20) were obtained from the Hamiltonian constraints at the shell, whereas Eq. (61) is an additional input that is not derived from the variational principle. A consistency check, for example by deriving the shell matching condition from the variation of the boundary terms in Eq. (12), should be provided before the metric-discontinuity conclusion can be accepted.
  3. [Section III.C, Eq. (21)] The gauge fixing (21) involves an arbitrary function f and a regulator l, and the paper asserts that the final dynamics is independent of l and that the final theory is defined by l -> 0. While the reduced action (33) and the evolution equation (38) indeed contain no l, the metric reconstruction in Section V.B uses the auxiliary point x0 and boundary conditions at x-l; whether the l -> 0 limit of the reconstructed metric is well-defined and independent of f is not demonstrated. Since the interpretation of the time coordinates t and t_- in Eq. (63) relies on this limit, the authors should either provide a justification or explicitly state the l -> 0 limit as an additional assumption.
minor comments (6)
  1. [Section V.B] The sentence 'This fact motives us to give up Eq. (61), and instead we impose (61)' appears to contain an equation-numbering error; the condition being abandoned should be Eq. (59), the induced-metric continuity condition, not the new condition (61).
  2. [Throughout, especially Eqs. (21)-(23) and (56)-(62)] The shell position and the radial coordinate are both denoted by x in many equations, making it difficult to distinguish the trajectory from the coordinate; please use a distinct symbol for the shell position consistently.
  3. [Eq. (32)] The second term of Theta(p, M) is written with M_+ while the function argument is M; if the function is intended to depend on a generic mass parameter, the subscript should be removed or the definition should be aligned with the argument.
  4. [Eq. (36) and Appendix B] The expression 'x - 2GM_-' should read 'x - 2M_-' since G = 1 has been set; the same inconsistency appears with 'GM' in Eq. (B5).
  5. [Eq. (57)] The symbol m is reused for sqrt(m^2+p^2), which creates ambiguity with the shell rest mass m defined in Eq. (11); using a different letter, such as mu, would improve readability.
  6. [Section VI] The first sentence contains a typo: 'o set the stage' should be 'To set the stage'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the shell trajectory follows from varying a reduced action, and the junction condition (61) is an openly imposed assumption rather than a disguised refit or a self-referential prediction.

full rationale

I walked the claimed derivation chain. The shell momentum p is determined by the junction condition (23), the reduced action (33) is then varied to obtain the equation of motion (38), and the bounce, spacelike segment, and horizon crossing are numerical outputs of (38), not inputs. No constant is fitted to the predicted trajectory, and no fitted parameter is renamed as a prediction. The gauge function f is chosen so that the junction conditions (19)-(20) hold; this is a consistency requirement, and the authors state the dynamics is independent of the regulator l. The one load-bearing choice is the junction rule in Eq. (61), where the paper explicitly says that requiring continuity of the reduced metric (Eq. (59)) would give a complex lapse at the bounce, so it 'instead we impose' Eq. (61). This is an assumption, not a circular derivation: Eq. (61) is not secretly identical to the results, and the metric discontinuity and finite horizon lifetime are presented as consequences of that imposed rule rather than as outputs of the effective dynamics alone. The paper also flags the limitation in Sec. VI, noting it is unknown whether the spacelike segment is physical or an artifact of the lack of covariance. Self-citations (e.g., [46] for a future covariant framework) are not load-bearing; the effective Hamiltonian and shell action are taken from external prior work [23, 39, 43]. Therefore the central derivation is not circular; the main concern is robustness of the imposed junction condition, which is a correctness question, not a circularity one.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The derivation rests on the polymerized effective Hamiltonian of [11,18], the classical dust-shell phase space of [39,43,45], a gauge choice with an arbitrary regulator function f, and an imposed junction condition (61). None of these are fitted to data; the model parameters are zeta, M+, M-, and m. The fragility lies in the assumptions, not in hidden fitting.

assumptions (6)
  • domain assumption The polymerized effective Hamiltonian Heff (Eq. (2)) with parameter zeta correctly describes vacuum spherically symmetric quantum-corrected gravity.
    Adopted from [11,18,23]; the action (1) and all subsequent dynamics rely on this input.
  • domain assumption The dust shell is described by canonical variables (x,p) with {x,p}=1 and Hamiltonian (11) from [39,43,45].
    Section III; the reduced action and equation of motion (38) follow from this phase space.
  • ad hoc to paper The gauge fixing (21) with an arbitrary function f satisfying conditions (i)-(iii) is admissible, and the final dynamics is independent of the regulator l.
    Section III.C; used to satisfy junction conditions; l-independence is asserted, not proven; the l to 0 limit defines the theory.
  • ad hoc to paper The junction condition (61) imposing continuity of the shell's proper time (absolute value of tangent norm) is the correct matching rule.
    Section V.B; chosen to keep lapse real at bounce; drives the metric discontinuity and time-coordinate mismatch claims.
  • domain assumption Fields EI, KI are smooth except at the shell, EI continuous there, with falloff (14) defining masses M+ and M-.
    Section III.B and III.A; standard junction setup; needed for the boundary action and junction conditions.
  • domain assumption The metric takes the PG form (8) in the vacuum regions, and the chosen sign of K2 selects ingoing PG coordinates.
    Section II; the coordinate interpretation of the shell trajectory and the comparison with [13,30] depend on this.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Dust shell in effective loop quantum black hole model." pith.science (2026). https://pith.science/paper/RTCUGSY2

@misc{pith2026250604589,
  author       = {Pith},
  title        = {Pith review of: Dust shell in effective loop quantum black hole model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RTCUGSY2}},
  note         = {Machine review of arXiv:2506.04589}
}
abstract

In this work, the dynamics of a dust shell in an effective theory of spherically symmetric gravity containing quantum corrections from loop quantum gravity is investigated. To provide a consistent framework for including the dust, we go beyond the standard formulation of the effective theory by introducing an action that includes not only the effective Hamiltonian constraint, but also the diffeomorphism constraint, along with appropriate gauge-fixing and boundary terms. By adding the dust shell action and substituting vacuum solutions for the interior and exterior regions, we derive a reduced action in which only the shell radius $\mathfrak{x}$ and the exterior black hole mass appear as dynamical variables. Varying the reduced action yields the evolution equation for $\mathfrak{x}$, which is then solved numerically to explore the dynamical properties of the dust shell and the continuity properties of the metric. Finally, our approach is compared with previous studies to highlight key differences and improvements.

Figures

Figures reproduced from arXiv: 2506.04589 by the authors.

Figure 1
Figure 1. Subsequently, the shell follows a spacelike path that crosses the outer horizon, re-emerging from the BH, and eventually transitions back to a timelike trajectory. An important consequence of the spacelike propagation of the dust shell is that the BH horizon becomes finite in duration, as indicated by the blue horizontal segment. In the case considered in [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Evolution of the dust shell radius [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The maximal value of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: According to the results, it can be concluded [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The difference between the Lagrangian of the dust [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The difference between the time coordinates [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

50 extracted references · 21 canonical work pages

  1. [1]

    Choose the gaugeE1 = x2 and solve the diffeomor- phism constraint Hx = 0 to get K1 = E2∂xK2/x

    work page

  2. [2]

    Substitute the expression of E1 and K1 into the classical Hamiltonian constraint, and do loop quan- tization to get the effective Hamiltonian constraint ˜Heff

    work page

  3. [3]

    Define matter density asρ ∝ ˜Heff

    work page

  4. [4]

    the Fundamental Research Funds for the Central Universities

    Find the weak solution to the Hamilton’s equation associated with ˜Heff to get the trajectory of the dust shell. Although the original procedure presented in the refer- ences differs from the one summarized here, the approach described above offers an equivalent alternative interpre- tation (see Sec. I). In this procedure, the˜Heff obtained in step 2) is ...

    work page

  5. [5]

    Background independent quantum gravity: A Status report,

    Abhay Ashtekar and Jerzy Lewandowski, “Background independent quantum gravity: A Status report,” Class. Quant. Grav. 21, R53 (2004), arXiv:gr-qc/0404018. 15

    arXiv 2004

  6. [6]

    Pr., Cambridge, UK, 2004)

    Carlo Rovelli,Quantum gravity, Cambridge Monographs on Mathematical Physics (Univ. Pr., Cambridge, UK, 2004)

    work page 2004

  7. [7]

    Fundamental structure of loop quantum gravity,

    Muxin Han, Weiming Huang, and Yongge Ma, “Fundamental structure of loop quantum gravity,” Int. J. Mod. Phys. D 16, 1397–1474 (2007), arXiv:gr-qc/0509064

    arXiv 2007

  8. [8]

    Thomas Thiemann, Modern Canonical Quantum General Relativity, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2007)

    work page 2007

Show all 50 references
  1. [9]

    Semiclassical loop quantum black hole,

    Leonardo Modesto, “Semiclassical loop quantum black hole,” Int. J. Theor. Phys.49, 1649–1683 (2010), arXiv:0811.2196 [gr-qc]

    2010 arXiv

  2. [10]

    Black holes in loop quantum gravity: The Complete space-time,

    Rodolfo Gambini and Jorge Pullin, “Black holes in loop quantum gravity: The Complete space-time,” Phys. Rev. Lett. 101, 161301 (2008), arXiv:0805.1187 [gr-qc]

    2008 arXiv

  3. [11]

    Loop quantization of the Schwarzschild interior revisited,

    Alejandro Corichi and Parampreet Singh, “Loop quantization of the Schwarzschild interior revisited,” Class. Quant. Grav. 33, 055006 (2016), arXiv:1506.08015 [gr-qc]

    2016 arXiv

  4. [12]

    Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections,

    Jibril Ben Achour, Suddhasattwa Brahma, and Antonino Marciano, “Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections,” Phys. Rev. D96, 026002 (2017), arXiv:1608.07314 [gr-qc]

    2017 arXiv

  5. [13]

    Quantum Transfiguration of Kruskal Black Holes,

    Abhay Ashtekar, Javier Olmedo, and Parampreet Singh, “Quantum Transfiguration of Kruskal Black Holes,” Phys. Rev. Lett. 121, 241301 (2018), arXiv:1806.00648 [gr-qc]

    2018 arXiv

  6. [14]

    Loop quantum Schwarzschild interior and black hole remnant,

    Cong Zhang, Yongge Ma, Shupeng Song, and Xiangdong Zhang, “Loop quantum Schwarzschild interior and black hole remnant,” Phys. Rev. D102, 041502(R) (2020), arXiv:2006.08313 [gr-qc]

    2020 arXiv

  7. [15]

    Effective loop quantum gravity framework for vacuum spherically symmetric spacetimes,

    Jarod George Kelly, Robert Santacruz, and Edward Wilson-Ewing, “Effective loop quantum gravity framework for vacuum spherically symmetric spacetimes,” Phys. Rev. D102, 106024 (2020), arXiv:2006.09302 [gr-qc]

    2020 arXiv

  8. [16]

    Loop quantum deparametrized Schwarzschild interior and discrete black hole mass,

    Cong Zhang, Yongge Ma, Shupeng Song, and Xiangdong Zhang, “Loop quantum deparametrized Schwarzschild interior and discrete black hole mass,” Phys. Rev. D105, 024069 (2022), arXiv:2107.10579 [gr-qc]

    2022 arXiv

  9. [17]

    Quantum Gravity of Dust Collapse: Shock Waves from Black Holes,

    Viqar Husain, Jarod George Kelly, Robert Santacruz, and Edward Wilson-Ewing, “Quantum Gravity of Dust Collapse: Shock Waves from Black Holes,” Phys. Rev. Lett.128, 121301 (2022), arXiv:2109.08667 [gr-qc]

    2022 arXiv

  10. [18]

    An effective model for the quantum Schwarzschild black hole,

    Asier Alonso-Bardaji, David Brizuela, and Raül Vera, “An effective model for the quantum Schwarzschild black hole,” Phys. Lett. B829, 137075 (2022), arXiv:2112.12110 [gr-qc]

    2022 arXiv

  11. [19]

    Reduced phase space quantization of black holes: Path integrals and effective dynamics,

    Cong Zhang, “Reduced phase space quantization of black holes: Path integrals and effective dynamics,” Phys. Rev. D104, 126003 (2021), arXiv:2106.08202 [gr-qc]

    2021 arXiv

  12. [20]

    Causal structure of a recent loop quantum gravity black hole collapse model,

    Johannes Münch, “Causal structure of a recent loop quantum gravity black hole collapse model,” Phys. Rev. D104, 046019 (2021), arXiv:2103.17112 [gr-qc]

    2021 arXiv

  13. [21]

    Towards a quantum notion of covariance in spherically symmetric loop quantum gravity,

    Rodolfo Gambini, Javier Olmedo, and Jorge Pullin, “Towards a quantum notion of covariance in spherically symmetric loop quantum gravity,” Phys. Rev. D105, 026017 (2022), arXiv:2201.01616 [gr-qc]

    2022 arXiv

  14. [22]

    Fate of quantum black holes,

    Viqar Husain, Jarod George Kelly, Robert Santacruz, and Edward Wilson-Ewing, “Fate of quantum black holes,” Phys. Rev. D106, 024014 (2022), arXiv:2203.04238 [gr-qc]

    2022 arXiv

  15. [23]

    Nonsingular spherically symmetric black-hole model with holonomy corrections,

    Asier Alonso-Bardaji, David Brizuela, and Raül Vera, “Nonsingular spherically symmetric black-hole model with holonomy corrections,” Phys. Rev. D106, 024035 (2022), arXiv:2205.02098 [gr-qc]

    2022 arXiv

  16. [24]

    Quantum Geometry and Black Holes,

    Rodolfo Gambini, Javier Olmedo, and Jorge Pullin, “Quantum Geometry and Black Holes,” (2023) arXiv:2211.05621 [gr-qc]

    2023 arXiv

  17. [25]

    Quantum Oppenheimer-Snyder and Swiss Cheese Models,

    Jerzy Lewandowski, Yongge Ma, Jinsong Yang, and Cong Zhang, “Quantum Oppenheimer-Snyder and Swiss Cheese Models,” Phys. Rev. Lett.130, 101501 (2023), arXiv:2210.02253 [gr-qc]

    2023 arXiv

  18. [26]

    Spacetime geometry from canonical spherical gravity,

    Asier Alonso-Bardaji and David Brizuela, “Spacetime geometry from canonical spherical gravity,” Phys. Rev. D109, 044065 (2024), arXiv:2310.12951 [gr-qc]

    2024 arXiv

  19. [27]

    Generalized analysis of a dust collapse in effective loop quantum gravity: fate of shocks and covariance,

    Kristina Giesel, Hongguang Liu, Parampreet Singh, and Stefan Andreas Weigl, “Generalized analysis of a dust collapse in effective loop quantum gravity: fate of shocks and covariance,” (2023), arXiv:2308.10953 [gr-qc]

    2023 arXiv

  20. [28]

    Embedding generalized LTB models in polymerized spherically symmetric spacetimes,

    Kristina Giesel, Hongguang Liu, Eric Rullit, Parampreet Singh, and Stefan Andreas Weigl, “Embedding generalized LTB models in polymerized spherically symmetric spacetimes,” (2023), arXiv:2308.10949 [gr-qc]

    2023 arXiv

  21. [29]

    A Covariant Approach to Singularity Resolution, Ph.D

    Asier Alonso Bardají, Loop Quantum Gravity Effects on Spherical Black Holes. A Covariant Approach to Singularity Resolution, Ph.D. thesis, U. Basque Country, Leioa (2023)

    2023

  22. [30]

    Shell-crossings and shock formation during gravitational collapse in effective loop quantum gravity,

    Francesco Fazzini, Viqar Husain, and Edward Wilson-Ewing, “Shell-crossings and shock formation during gravitational collapse in effective loop quantum gravity,” Phys. Rev. D109, 084052 (2024), arXiv:2312.02032 [gr-qc]

    2024 arXiv

  23. [31]

    Black holes and covariance in effective quantum gravity,

    Cong Zhang, Jerzy Lewandowski, Yongge Ma, and Jinsong Yang, “Black holes and covariance in effective quantum gravity,” Phys. Rev. D111, L081504 (2025), arXiv:2407.10168 [gr-qc]

    2025

  24. [32]

    Status of Birkhoff’s theorem in polymerized semiclassical regime of Loop Quantum Gravity,

    Luca Cafaro and Jerzy Lewandowski, “Status of Birkhoff’s theorem in polymerized semiclassical regime of Loop Quantum Gravity,” (2024), arXiv:2403.01910 [gr-qc]

    2024

  25. [33]

    Effective four-dimensional loop quantum black hole with a cosmological constant,

    Jianhui Lin and Xiangdong Zhang, “Effective four-dimensional loop quantum black hole with a cosmological constant,” Phys. Rev. D110, 026002 (2024), arXiv:2402.13638 [gr-qc]

    2024 arXiv

  26. [34]

    Gravitational collapse in effective loop quantum gravity: Beyond marginally bound configurations,

    Lorenzo Cipriani, Francesco Fazzini, and Edward Wilson-Ewing, “Gravitational collapse in effective loop quantum gravity: Beyond marginally bound configurations,” Phys. Rev. D110, 066004 (2024), arXiv:2404.04192 [gr-qc]

    2024 arXiv

  27. [35]

    Black holes and covariance in effective quantum gravity: A solution without Cauchy horizons,

    Cong Zhang, Jerzy Lewandowski, Yongge Ma, and Jinsong Yang, “Black holes and covariance in effective quantum gravity: A solution without Cauchy horizons,” (2024), arXiv:2412.02487 [gr-qc]

    2024

  28. [36]

    Mass inflation and strong cosmic censorship conjecture in the covariant quantum black hole,

    Jianhui Lin, Xiangdong Zhang, and Moisés Bravo-Gaete, “Mass inflation and strong cosmic censorship conjecture in the covariant quantum black hole,” (2024), arXiv:2412.01448 [gr-qc]

    2024 arXiv

  29. [37]

    Covariant effective spacetimes of spherically symmetric electro-vacuum with a cosmological constant,

    Jinsong Yang, Cong Zhang, and Yongge Ma, “Covariant effective spacetimes of spherically symmetric electro-vacuum with a cosmological constant,” (2025), arXiv:2503.15157 [gr-qc]. 16

    2025

  30. [38]

    Gentle spaghettification in effective LQG dust collapse,

    Francesco Fazzini, “Gentle spaghettification in effective LQG dust collapse,” (2025), arXiv:2502.20187 [gr-qc]

    2025 arXiv

  31. [39]

    Quantum induced shock dynamics in gravitational collapse: insights from effective models and numerical frameworks,

    Hongguang Liu and Dongxue Qu, “Quantum induced shock dynamics in gravitational collapse: insights from effective models and numerical frameworks,” (2025), arXiv:2504.18462 [gr-qc]

    2025 arXiv

  32. [40]

    On weak solutions in Einstein theory and beyond,

    Francesco Fazzini and Hassan Mehmood, “On weak solutions in Einstein theory and beyond,” (2025), arXiv:2505.01846 [gr-qc]

    2025

  33. [41]

    Higher-dimensional quantum Oppenheimer-Snyder model,

    Zijian Shi, Xiangdong Zhang, and Yongge Ma, “Higher-dimensional quantum Oppenheimer-Snyder model,” Phys. Rev. D 110, 104074 (2024), arXiv:2408.15821 [gr-qc]

    2024 arXiv

  34. [42]

    Singular hypersurfaces and thin shells in general relativity,

    W. Israel, “Singular hypersurfaces and thin shells in general relativity,” Nuovo Cim. B44S10, 1 (1966), [Erratum: Nuovo Cim.B 48, 463 (1967)]

    1966

  35. [43]

    Reduced phase space formalism for spherically symmetric geometry with a massive dust shell,

    John L. Friedman, Jorma Louko, and Stephen N. Winters-Hilt, “Reduced phase space formalism for spherically symmetric geometry with a massive dust shell,” Phys. Rev. D56, 7674–7691 (1997), arXiv:gr-qc/9706051

    1997 arXiv

  36. [44]

    thesis, Madrid U

    Adrián Casado-Turrión,Compact objects in modified gravity: junction conditions and other viability criteria, Ph.D. thesis, Madrid U. (2023), arXiv:2312.03757 [gr-qc]

    2023 arXiv

  37. [45]

    Covariant¯µ-scheme effective dynamics, mimetic gravity, and nonsingular black holes: Applications to spherically symmetric quantum gravity,

    Muxin Han and Hongguang Liu, “Covariant¯µ-scheme effective dynamics, mimetic gravity, and nonsingular black holes: Applications to spherically symmetric quantum gravity,” Phys. Rev. D109, 084033 (2024), arXiv:2212.04605 [gr-qc]

    2024 arXiv

  38. [46]

    Black holes in effective loop quantum gravity: Covariant holonomy modifications,

    Idrus Husin Belfaqih, Martin Bojowald, Suddhasattwa Brahma, and Erick I. Duque, “Black holes in effective loop quantum gravity: Covariant holonomy modifications,” (2024), arXiv:2407.12087 [gr-qc]

    2024 arXiv

  39. [47]

    Reduced Hamiltonian for intersecting shells,

    Francesco Fiamberti and Pietro Menotti, “Reduced Hamiltonian for intersecting shells,” Nucl. Phys. B794, 512–537 (2008), arXiv:0708.2868 [hep-th]

    2008 arXiv

  40. [48]

    Non-uniquenessoftheshockwavedynamicsineffectiveloopquantumgravity,

    FrancescoFazzini,“Non-uniquenessoftheshockwavedynamicsineffectiveloopquantumgravity,” (2025),arXiv:2502.03003 [gr-qc]

    2025 arXiv

  41. [49]

    Lagrangian and Hamiltonian formalism for discontinuous fluid and gravitational field,

    P. Hajicek and J. Kijowski, “Lagrangian and Hamiltonian formalism for discontinuous fluid and gravitational field,” Phys. Rev. D57, 914–935 (1998), [Erratum: Phys.Rev.D 61, 129901 (2000)], arXiv:gr-qc/9707020

    1998 arXiv

  42. [50]

    Covariant dynamics from static spherically symmetric geometries,

    Cong Zhang and Zhoujian Cao, “Covariant dynamics from static spherically symmetric geometries,” (2025), arXiv:2506.09540 [gr-qc]

    2025

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.