Pith. sign in

REVIEW 2 major objections 4 minor 2 cited by

This paper claims that generalized Oppenheimer-Snyder collapse into any static two-horizon exterior splits into three outcomes—singular, bouncing, soft-landing—determined by local conditions on the exterior metric.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

Generalized Oppenheimer-Snyder collapse into two-horizon exteriors splits into singular, bouncing, and soft-landing categories, with Reissner-Nordström showing the bounce and regular de Sitter-core black holes never doing so.

T0 review reviewed 2026-08-03 challenge →

load-bearing objection A coherent new classification of generalized homogeneous collapse, but the interior is not pressureless dust for non-Schwarzschild exteriors, so the central physical premise is wrong as written. the 2 major comments →

arxiv 2602.04956 v2 pith:6CBQT325 submitted 2026-02-04 gr-qc hep-th

Classification of Oppenheimer-Snyder Collapse: Singular, Bouncing, and Soft-Landing Scenarios

Zhi-Chao Li , H. Khodabakhshi , H. Lu This is my paper
classification gr-qc hep-th PACS 04.20.-q04.70.Bw
keywords Oppenheimer-Snyder collapseapparent horizonbouncesoft landingReissner-Nordströmregular black holesstrong cosmic censorshipmass function
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper studies gravitational collapse of a pressureless dust ball matched to a static, spherically symmetric exterior that has two horizons, and claims the late-time outcome is set by two local properties of the exterior. A bounce happens when the exterior's mass function crosses zero from below, so the surface stops at a finite radius and re-expands; an apparent-horizon vertex happens when the mass function obeys m'(R)R - 3m(R)=0, giving a temporary minimum of the horizon radius. For two-horizon exteriors, the paper argues that consistency of the trapped region forces the vertex to occur no earlier than the surface's inner-horizon crossing; for Reissner-Nordström this yields |q| ≥ √3 m/2 and a bounce at R*=q²/(2m). Regular black holes with de Sitter cores satisfying the null energy condition show neither feature, so their surfaces approach the center only as proper time goes to infinity. The paper classifies collapse as singular, bouncing, or soft-landing, and links bouncing to inner-horizon instability and strong cosmic censorship.

Core claim

For the generalized Oppenheimer-Snyder collapse of a dust ball matched to a special static exterior ds²=-f dt² + dr²/f + r² dΩ², the surface radius obeys dR/dT=-√(1-f(R)) and the apparent-horizon radius is RAH(R)=R/√(1-f(R)). The paper shows that two local conditions on f (equivalently on the mass function m=R(1-f)/2) decide the outcome: a bounce when f(R*)=1 with f'(R*)<0, i.e. m(R*)=0 and m'(R*)>0, and a left vertex of the apparent horizon when Rf'(R)+2(1-f(R))=0, i.e. m'(R)R-3m(R)=0. For two horizons, consistency requires the vertex to be no earlier than the inner-horizon crossing; in Reissner-Nordström this gives |q| ≥ √3 m/2 and a bounce at R*=q²/(2m). Regular black holes with de Sitter

What carries the argument

The central object is the exterior metric function f(r) of the two-horizon black hole and its associated mass function m(r)=r(1-f(r))/2. From f alone the paper derives the collapsing surface's velocity dR/dT=-√(1-f(R)) and the apparent-horizon radius RAH(R)=R/√(1-f(R)); differentiating gives the exact signature conditions: bounce at f=1 with f'<0, apparent-horizon vertex at Rf'+2(1-f)=0, and inflection radius at f'=0. The argument's engine is expressing these in terms of m and combining the null energy condition with regularity at the center to prove that dRAH/dT is nonpositive, so no vertex can appear.

Load-bearing premise

The load-bearing premise is the trapped-region consistency condition of Sec. 4.1: the apparent-horizon turning point must occur no earlier than the surface's crossing of the inner horizon. The paper motivates this by causality but does not derive it from the field equations; if a vertex-before-crossing ordering can be realized consistently, the parameter constraint |q| ≥ √3 m/2 and the classification of 'consistent' vertices would shift.

What would settle it

Run a fully nonlinear simulation of pressureless dust collapse matched to a Reissner-Nordström exterior, scanning charge in 0<|q|<m, and look for the apparent-horizon trajectory. If for some |q|<√3 m/2 the apparent-horizon radius has a local minimum before the surface crosses the inner horizon and the spacetime remains free of pathology, the paper's consistency constraint fails. Alternatively, construct a two-horizon special-static exterior satisfying the null energy condition with a regular core whose apparent-horizon slope dRAH/dT turns positive, contradicting the paper's monotonicity theore

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Every OS collapse into a static two-horizon exterior of the special static type ends as singular, bouncing, or soft-landing; no fourth late-time behavior appears in this framework.
  • For Reissner-Nordström exteriors, physical consistency forces the charge to satisfy |q| ≥ √3 m/2; in that range the collapse bounces at R* = q²/(2m) and shows an apparent-horizon vertex.
  • A bounce implies at least one apparent-horizon left vertex in asymptotically flat OS collapse, but a vertex can occur without a bounce.
  • Two horizons alone do not produce the new features: regular black holes with de Sitter cores under the null energy condition collapse monotonically and soft-land.
  • The paper argues that bouncing collapse implies matter accumulation and instability of the inner horizon, consistent with strong cosmic censorship, while cautioning that the classical bounce continuation inside the inner horizon may not survive in a realistic collapse.

Where Pith is reading between the lines

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

  • A fully dynamical numerical simulation of charged dust collapse could test the trapped-region ordering: if an apparent-horizon minimum appears before the surface reaches the inner horizon for charges below √3 m/2, the consistency condition would need to be revised.
  • The same local criteria could be applied to rotating or multi-horizon exteriors to see whether the three-way classification survives beyond spherical symmetry and the special static form.
  • If the classification is right, observing the exterior metric's behavior near a core—through gravitational-wave ringdown or lensing—could distinguish a soft-landing regular collapse from a singular one.
  • The theorem that Minkowski-core regular black holes violate the null energy condition is testable in principle by constraining the effective core equation of state; a detected Minkowski-core collapse would require NEC-violating matter.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper studies the dynamics of a collapsing homogeneous fluid sphere matched, via Israel junction conditions, to static spherically symmetric exteriors of the special form ds² = -f(r)dt² + f(r)^{-1}dr² + r²dΩ². Starting from the surface equation ˙R² = 1 - f(R), it derives local conditions for two possible signatures: an apparent-horizon left vertex (dR_AH/dT = 0, equivalent to m'(R)R - 3m(R) = 0) and a surface bounce (f(R*)=1, f'(R*)<0). These criteria are applied to Reissner-Nordström, where all three special radii R*, R_infl, R_turn are computed and ordered, and to regular black holes with de Sitter cores, where NEC excludes both signatures and the surface approaches the center only asymptotically. The paper classifies the outcomes as singular, bouncing, and soft-landing collapse, and argues consistency with Penrose's strong cosmic censorship conjecture.

Significance. Within its own framework the paper is quite clean: the local criteria are derived in an explicit, parameter-free way in Eqs. (9)-(20), and the RN section is internally consistent, with the three radii satisfying the stated ordering (38). The NEC-based monotonicity argument for de Sitter-core regular black holes in Sec. 5.1, and the resulting new proof that Minkowski-core regular black holes violate the NEC, are elegant and would be a useful contribution. The main limitation is that, as written, the model is not literal Oppenheimer-Snyder dust collapse for non-Schwarzschild exteriors; it is a homogeneous perfect-fluid collapse with nonzero pressure. This reframing does not destroy the technical derivations, but it changes the physical claims and the title/abstract. If the dust identification is corrected, the classification of surface outcomes and horizon behavior is a valuable addition to the OS-type collapse literature.

major comments (2)
  1. [Sec. 2, Eqs. (3)-(5)] The interior is not pressureless dust for any non-Schwarzschild exterior. With H = -sqrt(1-f(R))/R, the perfect-fluid pressure of the FLRW interior is p = -(2Hdot+3H²)/(8π) = [R f'(R) - (1-f(R))]/(8π R²). For the RN exterior (23) this gives p = -q²/(8π R⁴) ≠ 0; the regular-core examples in Sec. 5 and Appendices A/B also have nonzero pressure. Thus the matched solutions are homogeneous perfect-fluid interiors with generically negative pressure, not Oppenheimer-Snyder dust. The surface equations remain valid for this perfect-fluid model, but the repeated interpretation as 'pressureless dust' and as 'OS collapse' is incorrect unless f is Schwarzschild. The paper should either explicitly restrict the dust claim to f = 1-2M/r or redefine the model as a generalized OS-type perfect-fluid collapse and compute/discuss the interior pressure profile.
  2. [Sec. 4.1, Eq. (28)] The trapped-region consistency condition T(R_turn) ≥ T(R_-), which is then translated to R_turn ≤ R_- and to the RN bound |q| ≥ √3 m/2 in (30), is asserted as a physical necessity but not derived from the Israel junction conditions, the field equations, or the definition of the apparent horizon. This condition is load-bearing: it decides which of the two orderings in Fig. 1 is deemed physical and sets the parameter range for the 'consistent' RN bounce-with-vertex scenario. The authors should either prove this condition from a global causal/trapped-region argument or explicitly present it as an extra selection rule/assumption, and discuss how the classification changes if vertex-before-crossing configurations are admitted.
minor comments (4)
  1. [Sec. 6, first paragraph of Conclusion] The sentence 'for regular black holes, which necessarily have two horizons, their OS collapse has no apparent-horizon left vertex, nor any bounce' is too broad. Section 5.2 shows that Minkowski-core regular black holes (which violate NEC) have at least one left vertex. The claim should be qualified to 'regular black holes satisfying the NEC' or 'with de Sitter cores', which is how the abstract correctly phrases it.
  2. [Sec. 5.1, just before Eq. (39)] The statement that NEC implies f(r) ≤ 1 for regular black holes with inequality saturated at the core and at infinity is cited to Ref. [14] but not derived in this paper. A short derivation or a precise theorem statement would make the no-bounce argument self-contained.
  3. [Fig. 2 and Sec. 4.2.1] At the bounce radius R*, one has f(R*)=1, so R_AH = R/sqrt(1-f(R)) diverges as R→R*+. The figure and the surrounding text do not indicate this divergence; the apparent-horizon trajectory has a vertical asymptote at the bounce rather than a smooth return. A brief note or a zoomed inset would prevent the reader from misreading the diagram.
  4. [Appendix A, action (50)] There is a typo in the field-strength definition: 'F_μν = ∂_μ A_ν − ∂_μ A_ν' should be '∂_μ A_ν − ∂_ν A_μ'.

Circularity Check

0 steps flagged

No significant circularity: all classification criteria are derived from the exterior metric function and are not fitted or self-referential.

full rationale

The derivation chain is self-contained. The surface equation Rdot^2=1-f(R), Eq. (5), follows from the stated Israel junction conditions for the FLRW interior, and the bounce and vertex criteria (12), (15), (17) are obtained by direct differentiation of this equation and of the apparent-horizon formula (7). The RN results (R*=q^2/2m, R_turn=2q^2/3m, R_infl=q^2/m) are explicit algebraic evaluations of those criteria for the RN metric (23), not fitted parameters later called predictions. The regular-black-hole no-vertex theorem is proven within the paper from the NEC inequality (40) and the regularity condition (42), and the Minkowski-core no-go result is a contradiction between that proven no-vertex statement and the vertex implied by the Minkowski-core expansion (48)-(49). Citations to [3], [6], and [14] are to prior derivations with stated assumptions (junction conditions, dust interior, NEC) and none of those assumptions contains the target classification, so they are not circular. The serious concern that non-Schwarzschild exteriors require a non-dust interior with nonzero pressure is a physical correctness issue, not a circularity of the derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

No parameters are fitted to data; m, q, alpha, and the critical masses are free example parameters, not fitted values. The analysis rests on the special-static metric restriction from [3], the standard dust/Friedmann interior, the imported NEC characterization of regular black holes from [14], and the paper's own trapped-region time-ordering condition, which is the most paper-specific and least-derived input.

axioms (6)
  • domain assumption The exterior metric is restricted to the special static form ds^2 = -f(r)dt^2 + dr^2/f(r) + r^2 dOmega^2 (h=f).
    The generalized OS matching requires h=f; the paper cites [3] for this requirement and does not re-derive it. All examples and classification results depend on this metric restriction.
  • domain assumption The interior is a spatially flat (k=0) FLRW pressureless dust ball in Painleve-Gullstrand slicing.
    This is the standard OS idealization used in Eqs. (3)-(5); it fixes the form of the apparent horizon R_AH = 1/|H| and the surface equation (5).
  • ad hoc to paper The trapped-region consistency condition T(R_turn) >= T(R_-) (Eq. 28) is physically necessary.
    This condition is asserted as the criterion for a consistent vertex and drives the RN charge bound |q| >= sqrt(3)m/2. It is argued from a trapped-region picture but not derived from the field equations or from a formal definition of the trapped region.
  • domain assumption For regular black holes satisfying the NEC, the core must be de Sitter and f(r) <= 1, with equality at infinity and at the core.
    Imported from the authors' prior work [14]; used in Sec. 5.1 to rule out a bounce and to prove the no-vertex monotonicity result.
  • domain assumption Regular centers satisfy m(0)=0 and m(r)=O(r^3) as r->0.
    This regularity condition is used in the integration inequality (43)-(44) that yields G(r)>=0 and hence no left vertex.
  • domain assumption The collapsing surface starts from a sufficiently large, asymptotically flat initial radius R0.
    Used in the bounce=>left-vertex proof of Sec. 3.3 and in the Minkowski-core-vertex argument, where asymptotic flatness fixes dR_AH/dT -> -3/2 at early times.

reviewed 2026-08-03 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Classification of Oppenheimer-Snyder Collapse: Singular, Bouncing, and Soft-Landing Scenarios." pith.science (2026). https://pith.science/paper/6CBQT325

@misc{pith2026260204956,
  author       = {Pith},
  title        = {Pith review of: Classification of Oppenheimer-Snyder Collapse: Singular, Bouncing, and Soft-Landing Scenarios},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6CBQT325}},
  note         = {Machine review of arXiv:2602.04956}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

We study Oppenheimer-Snyder (OS) gravitational collapse matched to a general static, spherically symmetric exterior spacetime. Unlike the Schwarzschild case, two new features can arise in black holes with two horizons: an apparent-horizon minimum, a temporary minimum in the apparent-horizon radius during collapse, and a bounce, where the star surface stops collapsing at a nonzero radius and reverses into expansion. We identify the conditions that lead to these two features. For two-horizon exteriors, trapped-region consistency requires that the apparent-horizon turning point occurs no earlier than the surface crossing of the inner horizon. As a concrete example, the OS collapse of the Reissner-Nordstr\"om (RN) spacetime shows both effects. In contrast, regular black holes with de Sitter cores show neither: their collapse is smooth and monotonic, and the surface approaches the center only as the proper time goes to infinity. These results naturally classify the OS collapses into three categories: singular, which ends at the center in finite time; bouncing, which reverses at a finite radius; and soft-landing, which reaches the center only asymptotically. We argue that these features are consistent with Penrose's strong cosmic censorship conjecture.

Figures

Figures reproduced from arXiv: 2602.04956 by H. Khodabakhshi, H. Lu, Zhi-Chao Li.

Figure 1
Figure 1. Figure 1: Depending on the charges, two possible time orderings between the apparent-horizon turning point and the inner-horizon crossing in RN OS collapse with m = 1 (left: q = 0.65; right: q = 0.95). The black curve is the star-surface trajectory (R, T(R)), while the red curve is the apparent-horizon trajectory RAH(R), T(R)  . The condition (29) is a global consistency requirement: it ensures that the relevant in… view at source ↗
Figure 2
Figure 2. Figure 2: RN collapse in the (R, T) plane. The initial radius is R0 = 4.5, and the inner and outer horizons are set to (R−, R+) = (0.5, 1.5). These choices fix the mass and charge as m = (R++R−)/2 = 1 and q 2 = R+R− = 0.75. The collapse features three key radii: the surface bounce radius R∗ = 0.375, the apparent-horizon vertex Rturn = 0.5 = R−, and the inflection point Rinfl = 0.75. The black curve shows the star su… view at source ↗
Figure 3
Figure 3. Figure 3: Collapse diagram in the (R, T) plane for a electrically-charged regular black hole in EMS gravity with (n, α) = (1, 1) and (q, m) = (15, mcr(15)), starting from R0 = 40. The vertical lines indicate the horizon radii R± in (53). The star surface R(T) (black) exhibits no turning point and thus no bounce. The apparent-horizon curve RAH(T) (pink) is monotone and has no left vertex. The inflection radius Rinfl … view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Matter Maps to Geometry in Gravitational Collapse

    gr-qc 2026-05 unverdicted novelty 5.0

    An exact bidirectional algebraic map exists between the interior Friedmann density of a collapsing star and its exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse.

  2. Matter Maps to Geometry in Gravitational Collapse

    gr-qc 2026-05 unverdicted novelty 5.0

    Darmois–Israel junction conditions yield an exact bidirectional algebraic map from homogeneous interior density to exterior metric functions in generalized Oppenheimer–Snyder collapse.

Reference graph

Works this paper leans on

21 extracted references · 1 canonical work pages · cited by 1 Pith paper

  1. [1]

    On continued gravitational contraction,

    J.R. Oppenheimer and H. Snyder, “On continued gravitational contraction,” Phys. Rev. 56(1939) 455–459, doi:10.1103/PhysRev.56.455

    doi:10.1103/physrev.56.455 1939

  2. [2]

    Singular hypersurfaces and thin shells in general relativity,

    W. Israel, “Singular hypersurfaces and thin shells in general relativity,” Nuovo Cim. B 44S10(1966) 1 [erratum: Nuovo Cim. B48(1967) 463], doi:10.1007/BF02710419

    doi:10.1007/bf02710419 1966

  3. [3]

    The upper bound of event horizon formation time in generalized Oppenheimer-Snyder collapse,

    Z.C. Li, H. Khodabakhshi and H. L¨ u, “The upper bound of event horizon formation time in generalized Oppenheimer-Snyder collapse,” [arXiv:2512.24421 [gr-qc]], to appear in PLB

    arXiv

  4. [4]

    Nonsingular general relativistic gravitational collapse,

    J. Bardeen, “Nonsingular general relativistic gravitational collapse,” in Proceedings of the International Conference GR5, Tbilisi, U.S.S.R. (1968), p. 174

    1968

  5. [5]

    Formation and evaporation of non-singular black holes,

    S.A. Hayward, “Formation and evaporation of non-singular black holes,” Phys. Rev. Lett. 96(2006) 031103, doi:10.1103/PhysRevLett.96.031103, [arXiv:gr-qc/0506126 [gr-qc]]

    Pith/arXiv arXiv 2006

  6. [6]

    Gravitational collapse: generalizing Oppenheimer Snyder and a conjecture on horizon formation time,

    H. Khodabakhshi, H. L¨ u and F. Shojai, “Gravitational collapse: generalizing Oppenheimer Snyder and a conjecture on horizon formation time,” Phys. Rev. D12(2025) 124057, doi:10.1103/PhysRevD.112.124057, [arXiv:2506.03702 [gr-qc]]

    arXiv 2025

  7. [7]

    Penrose,Singularities of Spacetime, Theoretical Principles in Astro physics and Rela- tivity(A78-43851 19-90), Chicago University Press, Chicago, 1978

    R. Penrose,Singularities of Spacetime, Theoretical Principles in Astro physics and Rela- tivity(A78-43851 19-90), Chicago University Press, Chicago, 1978

    1978

  8. [8]

    Hawking, W

    S.W. Hawking, W. Israel,General Relativity, an Einstein Centenary Survey,Cambridge University Press, Cambridge, 1979

    1979

  9. [9]

    The question of cosmic censorship,

    R. Penrose, “The question of cosmic censorship,” Gen. Rel. Grav.34(2002) 1141, doi:10.1023/A:1016346228772. 21

    work page doi:10.1023/a:1016346228772 2002

  10. [10]

    Relativistic equations for adiabatic, spherically sym- metric gravitational collapse,

    C.W. Misner and D.H. Sharp, “Relativistic equations for adiabatic, spherically sym- metric gravitational collapse,” Phys. Rev.136(1964) B571–B576, doi:10.1103/Phys Rev.136.B571

    doi:10.1103/phys 1964

  11. [11]

    Regular electric black holes from Einstein-Maxwell-scalar grav- ity,

    Z.C. Li and H. L¨ u, “Regular electric black holes from Einstein-Maxwell-scalar grav- ity,” Phys. Rev. D110, no.10, 104046 (2024) doi:10.1103/PhysRevD.110.104046 [arXiv:2407.07952 [gr-qc]]

    Pith/arXiv arXiv 2024

  12. [12]

    Generalized Oppenheimer-Snyder gravi- tational collapse into regular black holes,

    F. Shojai, A. Sadeghi and R. Hassannejad, “Generalized Oppenheimer-Snyder gravi- tational collapse into regular black holes,” Class. Quantum Grav.39(2022) 085003, doi:10.1088/1361-6382/ac5924, [arXiv:2202.14024 [gr-qc]]

    Pith/arXiv arXiv 2022

  13. [13]

    Internal structure of black holes,

    E. Poisson and W. Israel, “Internal structure of black holes,” Phys. Rev. D41(1990) 1796–1809, doi:10.1103/PhysRevD.41.1796

    doi:10.1103/physrevd.41.1796 1990

  14. [14]

    Regular black holes from analyticf(F 2),

    Z.C. Li and H. L¨ u, “Regular black holes from analyticf(F 2),” Eur. Phys. J. C83(2023) no.8, 755 doi:10.1140/epjc/s10052-023-11908-x [arXiv:2303.16924 [gr-qc]]

    Pith/arXiv arXiv 2023

  15. [15]

    Foundations of the new field theory,

    M. Born and L. Infeld, “Foundations of the new field theory,” Proc. Roy. Soc. Lond. A 144(1934) 425–451, doi:10.1098/rspa.1934.0059

    arXiv 1934

  16. [16]

    Born-Infeld black holes in the presence of a cosmological constant,

    T.K. Dey, “Born-Infeld black holes in the presence of a cosmological constant,” Phys. Lett. B595(2004) 484–490, doi:10.1016/j.physletb.2004.06.047, [arXiv:hep-th/0406169 [hep-th]]

    Pith/arXiv arXiv 2004

  17. [17]

    Quasi-topological electromagnetism: dark energy, dyonic black holes, stable photon spheres and hidden electromagnetic duality,

    H.S. Liu, Z.F. Mai, Y.Z. Li and H. L¨ u, “Quasi-topological electromagnetism: dark energy, dyonic black holes, stable photon spheres and hidden electromagnetic duality,” Sci. China Phys. Mech. Astron.63, 240411 (2020) doi:10.1007/s11433-019-1446-1 [arXiv:1907.10876 [hep-th]]

    Pith/arXiv arXiv 2020

  18. [18]

    Regular black hole in general relativity coupled to nonlin- ear electrodynamics,

    E. Ay´ on-Beato and A. Garc ´ ıa, “Regular black hole in general relativity coupled to nonlin- ear electrodynamics,” Phys. Rev. Lett.80(1998) 5056–5059, doi:10.1103/PhysRevLett. 80.5056, [arXiv:gr-qc/9911046 [gr-qc]]

    Pith/arXiv arXiv 1998

  19. [19]

    New regular black hole solution from nonlinear electrody- namics,

    E. Ay´ on-Beato and A. Garc ´ ıa, “New regular black hole solution from nonlinear electrody- namics,” Phys. Lett. B464(1999) 25–29, doi:10.1016/S0370-2693(99)01038-2, [arXiv:hep- th/9911174 [hep-th]]

    arXiv 1999

  20. [20]

    Construction of regular black holes in general relativity,

    Z.Y. Fan and X. Wang, “Construction of regular black holes in general relativity,” Phys. Rev. D94, no.12, 124027 (2016) doi:10.1103/PhysRevD.94.124027 [arXiv:1610.02636 [gr- qc]]. 22

    Pith/arXiv arXiv 2016

  21. [21]

    Regular black holes from pure gravity,

    P. Bueno, P.A. Cano and R.A. Hennigar, “Regular black holes from pure gravity,” Phys. Lett. B861(2025), 139260 doi:10.1016/j.physletb.2025.139260 [arXiv:2403.04827 [gr-qc]]. 23

    arXiv 2025

This paper was first reviewed by deepseek-v4-flash on August 3, 2026.