Pith. sign in

REVIEW 3 major objections 5 minor 2 cited by

On new regular charged black hole solutions: Limiting Curvature Condition, Quasinormal modes and Shadows

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read The paper constructs two new regular charged black hole solutions from nonlinear electrodynamics, then derives two further solutions that satisfy the Limiting Curvature Condition, keeping curvature invariants bounded by a universal scale…

desk verdict Two new regular charged black hole metrics are real and carefully worked out, but the LCC claim for the second solution rests on an unproven finite-M bound, and the stability of the first solution is asserted by analogy rather than shown. read the letter →

arxiv 2412.00550 v1 pith:JXLLEQYE submitted 2024-11-30 gr-qc

Leonardo Balart , Grigoris Panotopoulos , Angel Rincon This is my paper · ORCID
classification gr-qc MSC 83C5783C22 PACS 04.70.-s04.40.Nr
keywords regularblackholesnonlinearelectrodynamicslimitingcurvatureconditionenergyconditionsquasinormalmodesholeshadowdynamicstabilityextremalcharge
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

The paper sets out to show that four-dimensional general relativity coupled to nonlinear electrodynamics admits regular charged black hole solutions whose curvature invariants remain bounded by a universal constant $B\ell^{-2}$ even when the mass $M$ is taken to infinity, and claims these are the first such four-dimensional solutions. Two new spherically symmetric metric functions are introduced, with their nonlinear electrodynamics Lagrangians given explicitly, and each solution is tested for dynamic stability against arbitrary linear fluctuations and for the null, weak, dominant, and strong energy conditions. From these charged solutions, two further regular solutions are constructed by replacing the charge $q$ with a fundamental length $\ell$, and their Ricci and Kretschmann scalars are shown to approach finite values proportional to $\ell^{-2}$ and $\ell^{-4}$ as $M\to\infty$. If the construction holds, regular charged black holes can evade unbounded curvature growth at the center, and the computed shadow radii and quasinormal frequencies give testable signatures.

What carries the argument

The central objects are two mass functions giving the metric functions $f_1(r)$ and $f_2(r)$, together with their explicit nonlinear electrodynamics Lagrangians $L(F)$ (Eqs. 7 and 27), which reduce to Maxwell's $L\to F$ in the weak-field limit. The Moreno–Sarbach inequalities (12)–(15) on the Lagrangian viewed as a function of $x=q^2/r^2$ are used to decide dynamic stability. The Limiting Curvature Condition versions are obtained by the formal substitution $q\to\ell$ in the metric functions; since the Lagrangians are not recomputed for the LCC versions, all claims about their energy conditions and regularity rest on the substitution preserving the structure of the charged solutions. Finally, the eikonal limit of the WKB method connects quasinormal frequencies to the angular velocity $\Omega_c=\sqrt{f(r_{\rm ph})}/r_{\rm ph}$ and the Lyapunov exponent of the unstable circular photon orbit, with the shadow radius $R_{\rm sh}=1/\Omega_c$.

What would settle it

Derive the nonlinear-electrodynamics Lagrangian $L(F)$ directly from the LCC metric $f_I(r)$ or $f_{II}(r)$ and test the four Moreno–Sarbach inequalities (12)–(15) for all $x=q^2/r^2$ between the center and the outer horizon; a single violation for a parameter value the paper lists as stable would refute the stability claim.

Watch

Extended reading notes

Core claim

The central claim is that the two metric functions $f_1(r)=1-432M^4r^2/(432M^4q^2+(6Mr+q^2)^3)$ and $f_2(r)=1-(2M/r)(1-Mq^2/(Mq^2+8r^3)-q^2r^3/(2M(q^2+r^2)^2))$ describe regular charged black holes in general relativity with nonlinear electrodynamics, and that the two metrics obtained by the replacement $q\to\ell$ satisfy the Limiting Curvature Condition. In the first LCC solution, as $M\to\infty$, the Ricci scalar tends to $12/\ell^2$ and the Kretschmann scalar to $24/\ell^4$; for the second, the corresponding limits near the center are $192/\ell^2$ and $6144/\ell^4$ for small $\ell$. The authors further assert that solution 1 satisfies the weak energy condition everywhere and the strong energy condition outside the horizon for all charges below its extremal value $q_{\rm ext}=0.6458M$, while solution 2 is dynamically stable only for $q<0.9296M$ and is unstable between $0.9296M$ and its extremal charge $q_{\rm ext}=2.5379M$.

Load-bearing premise

The LCC solutions are made by substituting the length scale $\ell$ for the charge $q$ in the two charged metrics, and the paper assumes this substitution produces physically valid regular charged black holes whose nonlinear-electrodynamics Lagrangians remain well-defined and whose stability and energy-condition behavior is unchanged, even though the explicit $L(F)$ for the LCC models is not given.

Editorial extensions

If this is right

  • If the LCC construction is valid, these four metrics are concrete realizations of the conjecture that no spacetime curvature invariant can exceed a universal value set by a fundamental length, independent of the black hole's mass.
  • For solution 2, charges in the window $0.9296M \le q \le 2.5379M$ are dynamically unstable, so regular charged black holes in this family cannot persist with such charge-to-mass ratios.
  • The computed shadow radii and eikonal quasinormal frequencies for charges $0.6423M$ and $0.6458M$ give quantitative differences between the two solutions that future horizon-scale observations could in principle test.
  • The energy-condition results delimit the parameter ranges where the weak, dominant, and strong energy conditions hold, so any attempt to embed these metrics in a broader theory must respect those ranges.

Reading between the lines

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

  • Because the LCC Lagrangians are never written down, the construction may hold only at the level of the metric; a natural next step would be to test whether the Moreno–Sarbach stability inequalities survive the substitution $q\to\ell$.
  • The two LCC metrics, with curvature caps set by $\ell$, could serve as effective interior geometries for collapsed objects in any theory where a fundamental length regulates curvature, not just in the specific electrodynamics models used here.
  • If the eikonal QNM–shadow correspondence holds for these solutions, then a combined measurement of a shadow radius and a ringdown frequency would distinguish solution 1 from solution 2, since their predicted radii differ by about five percent at the same charge.
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 / 5 minor

Summary. The manuscript constructs two static, spherically symmetric regular black hole metrics, f1(r) in Eq. (4) and f2(r) in Eq. (24), together with nonlinear electrodynamics Lagrangians/Hamiltonians for both magnetic and electric interpretations. For each solution the authors analyze dynamic stability via the Moreno–Sarbach inequalities (12)–(15), compute the Ricci and Kretschmann scalars, and test the standard energy conditions. They then replace the charge q by a fundamental length ℓ to obtain two further metrics, Eqs. (39) and (40), and claim these are the first four-dimensional regular charged black hole solutions satisfying the Limiting Curvature Condition, with M→∞ curvature limits R→12/ℓ², K→24/ℓ⁴ and R→192/ℓ², K→6144/ℓ⁴. The paper closes with a computation of null geodesics, shadow radii, and eikonal quasinormal frequencies for the two LCC metrics.

Significance. If the main claims are correct, the paper would supply explicit analytic examples of regular charged black holes whose curvature invariants remain bounded by a fixed length scale as the mass grows without bound, a property that is often stated but rarely verified with closed-form bounds. The explicit metric functions and Lagrangians, the extremal-charge behavior of the second solution, and the reported instability window are useful concrete data for the regular-black-hole and NED literature. The weaknesses are concentrated in two load-bearing places: the LCC property for the second solution is only checked in the M→∞ limit, and the dynamic stability of the first solution is asserted rather than demonstrated. The shadow and eikonal QNM section is standard and adds little beyond tabulated values.

major comments (3)
  1. [Section 3, Eq. (40)] The LCC property of the second solution is not established. The Limiting Curvature Condition requires |R| ≤ Bℓ⁻² and |K| ≤ B'ℓ⁻⁴ for all finite M and all r, but the argument in Section 3 only quotes the M→∞ limits from Eqs. (32)–(33) and the small-ℓ values 192/ℓ² and 6144/ℓ⁴ in Eq. (42). The statement that the Kretschmann scalar has a global maximum in 0 < r < 5M/672 gives no information about how that maximum depends on M/ℓ, and it does not exclude a bump at intermediate M that exceeds the M→∞ value. Please provide an analytic proof of a uniform bound, or a high-resolution numerical scan over M/ℓ and r, before claiming that f_II(r) satisfies the LCC.
  2. [Section 2.1, Dynamic stability] For the first solution, the paper does not verify inequalities (14) and (15). The text says that the verification is 'analogous to what is shown in the graphs presented for the subsequent black hole solution', but the Lagrangian L(x) in Eq. (11) is structurally different from L(x) in Eq. (29), so the analogy is not a proof. No stability threshold is reported for solution 1, and no graph or analytic bound for L_xx and 3L_x − xf(x)L_xx is given. Since the abstract advertises a dynamic-stability analysis for each solution, this omission is load-bearing and should be fixed.
  3. [Section 3] The LCC metrics are presented as NED-based regular charged black hole solutions, but their Lagrangians are not written down explicitly and their validity as NED solutions is only inferred from the substitution q→ℓ. In particular, the dynamic stability of the LCC models is not checked: the thresholds obtained in Section 2 are for the original Lagrangians with charge q, and the paper does not state that the inequalities (12)–(15) remain valid after q is replaced by ℓ. If the substitution makes the Lagrangian ill-defined or unstable in the relevant parameter range, the physical interpretation of Eqs. (39)–(40) as regular charged black holes is unsupported. Please give the explicit L(F) for the LCC models and verify the stability inequalities, or state clearly which stability properties are being assumed.
minor comments (5)
  1. [Section 2.1, Eq. (15)] The stability condition (15) contains an undefined f(x); if the intended condition is 3L_x ≥ x L_xx, please correct it. The caption of Fig. 3 also garbles this expression ('3L x-x f(x)L xx)'), which should be written cleanly.
  2. [Section 2.2, after Eq. (32)] The text says the M→∞ limit of the Ricci scalar 'presents a global maximum at r=0 whose value is 180/q² as well as a finite global maximum value'. This is internally inconsistent: the expression in Eq. (32) tends to 192/q² as r→∞, which is larger than 180/q², so the global maximum is not at r=0. Please correct this sentence.
  3. [Section 2.1, Energy conditions] The range '0.642245M ≥ q ≥ qext = 0.6458M' has the inequality directions reversed; it should read 0.642245M ≤ q ≤ 0.6458M.
  4. [Section 4 and Conclusions] Table 1 and the conclusions repeatedly refer to 'electric charge', but Section 2 warns that the electric versions of the NED models require different Lagrangians in different regions and suffer from the problems discussed in Ref. [8]. The authors should clarify whether the shadow and QNM results, and the 'charged' designation, apply to the magnetic interpretation, the electric interpretation, or both.
  5. [Throughout] There are several typographical errors, including 'Laypunov' for Lyapunov, 'differencies' for differences, and 'discussed'/'sketch' minor phrasing issues. A careful proofreading pass is recommended.

Circularity Check

2 steps flagged · score 4.0 of 10

Partial circularity in the LCC claim: 'satisfies LCC' is equated with R,K ∝ ℓ^{-2},ℓ^{-4} limits obtained by q→ℓ substitution, while finite-M uniform bounds are left unproven; the energy/stability/shadow analysis is independent.

  1. self definitional [Section 5 (Conclusions), supported by Section 3, Eqs. (39)-(42)]
    "We then confirm by direct inspection that both cases satisfy the limit curvature condition (i.e. in both cases we obtain R ∝ ℓ−2 and K ∝ ℓ−4)."

    The Introduction defines LCC as the uniform bound |R| ≤ Bℓ^{-2} for all values of the solution parameters, with B independent of the specific solution. The verification in Section 3 only computes the M→∞ limits of R and K after the q→ℓ substitution (Eqs. (41)-(42)), and the Conclusions then identify 'satisfy the LCC' with 'R ∝ ℓ^{-2}, K ∝ ℓ^{-4}'. This replaces the required all-M, all-r bound by a scaling law that the ansatz was designed to exhibit; for solution 2, Eq. (42) is the M→∞ large-r limit of Eqs. (32)-(33), and no finite-M global maximum is bounded. The central LCC claim thus rests on a self-defined criterion rather than on the stated LCC inequality.

  2. other [Section 3, Eqs. (39)-(42)]
    "We can use the results already obtained by replacing the charge q with the parameter ℓ in the previous section to confirm that these solutions do indeed satisfy the limit curvature condition."

    The LCC models are the same charged metrics (4) and (24) with q→ℓ, so the quoted curvature bounds are inherited from the ansatz, not derived as a consequence of an independent physical condition. For solution 2 the paper only states that K has a global maximum in 0<r<5M/672 without giving its value as a function of M/ℓ; it therefore never proves that |K| ≤ 6144/ℓ⁴ for all finite M. Presenting the substitution step as 'confirm' makes the LCC satisfaction a design feature rather than a verified result.

full rationale

The paper's core output is a pair of reverse-engineered regular black hole metrics with explicit NED Lagrangians (Eqs. (7) and (27)); deriving L(F) from a chosen f(r) is standard construction, not circularity. The energy-condition and Moreno-Sarbach stability checks are genuine consistency tests because not every reverse-engineered L(F) passes them. The shadow and eikonal QNM numbers follow from the metric via standard geodesic/WKB formulas and involve no fitting to data, so those parts are self-contained. The circularity is confined to the LCC claim. Section 3 constructs fI and fII by replacing the charge q with the length parameter ℓ and then 'confirms' LCC from the M→∞ values of R and K. The Introduction's LCC requires |R|≤Bℓ^{-2} for all M and all r; the Conclusions explicitly equate LCC with 'R∝ℓ^{-2}, K∝ℓ^{-4}', a weaker self-defined criterion. For solution 2, the quoted constants are M→∞ large-r limits, and the finite-M Kretschmann maximum is located but never bounded, so the headline 'first time' claim is not established. This is a genuine gap and a mild self-definitional circularity, but it does not infect the rest of the derivation chain; no load-bearing self-citation is involved, and no prediction is a renamed fit.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central construction rests on treating the metric functions as given and deriving the NED model from them; no new particles or forces are introduced. The main load-bearing assumptions are the validity of the Moreno-Sarbach stability criteria, the LCC as a requirement, the perfect-fluid interpretation of the anisotropic NED stress tensor, and the mapping q-to-ell preserving physical validity.

free parameters (1)
  • ell (fundamental length scale) = not fitted; chosen by hand
    Introduced in Section 3 by replacing the charge q with ell in the charged solutions to enforce the Limiting Curvature Condition. Its numerical value is not determined by any data or independent physics in the paper.
assumptions (4)
  • domain assumption General relativity coupled to nonlinear electrodynamics (NED) is the correct framework for the solutions.
    The entire construction assumes Einstein equations sourced by an NED Lagrangian, as stated in Sections 1 and 2.
  • domain assumption The Moreno-Sarbach inequalities (12)-(15) are necessary and sufficient for dynamic stability of regular black holes in self-gravitating NED.
    Used in Section 2 for both solutions, citing ref [43]. The paper applies them as a black-box criterion.
  • domain assumption The Limiting Curvature Condition is a physically required constraint on regular black holes.
    The paper treats LCC as a desirable condition from refs [51-53] and builds solutions specifically to satisfy it without independent justification.
  • domain assumption The energy-momentum tensor can be represented as a perfect fluid, T^i_j = diag(-rho, p1, p2, p3) with p1=-rho.
    Used in Section 2 to translate energy conditions into inequalities on rho and pressures, relying on spherical symmetry and the NED form.

how reviews work

0 comments
Cite this review

Pith. "Pith review of On new regular charged black hole solutions: Limiting Curvature Condition, Quasinormal modes and Shadows." pith.science (2026). https://pith.science/paper/JXLLEQYE

@misc{pith2026241200550,
  author       = {Pith},
  title        = {Pith review of: On new regular charged black hole solutions: Limiting Curvature Condition, Quasinormal modes and Shadows},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JXLLEQYE}},
  note         = {Machine review of arXiv:2412.00550}
}
read the original abstract

We introduce two new static, spherically symmetric regular black hole solutions that can be obtained from non-linear electrodynamics models. For each solution, we investigate the dynamic stability with respect to arbitrary linear fluctuations of the metric and electromagnetic field, and also examine the energy conditions that those black holes satisfy. Moreover, based on those solutions, we present two additional ones that satisfy the Limiting Curvature Condition. Finally, we make a comparison between the two solutions exploring their null geodesics and circular photon orbits.

Figures

Figures reproduced from arXiv: 2412.00550 by the authors.

Figure 1
Figure 1. The solid line illustrates the metric function for a case where [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. A plot of the quantity 4π(ρ − p2) as a function of r is shown for various values of q for the metric function f1(r). We choose M = 1 and q = 0.4, 0.5, 0.6 (green, blue, red) and q = qext = 0.6458 (black). Colored vertical arrows indicate the corresponding event horizons. In the expanded view box it is observed that as the electric charge decreases, the condition depicted in the figure ceases to be met (it takes nega… view at source ↗
Figure 3
Figure 3. For each of the conditions indicated in Eqs. (12) to (15), the black curve, corre [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Evaporating cosmologically coupled black holes

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    If a black hole's mass grows with cosmic expansion, Hawking evaporation is slowed or reversed, weakening gamma-ray bounds on primordial black holes.

  2. Charged black holes in Kalb-Ramond gravity: Weak Deflection Angle, Shadow cast, Quasinormal Modes and Neutrino annihilation

    gr-qc 2025-05 reject novelty 4.0 of 10

    The Kalb-Ramond black hole phenomenology is mostly an extension of known results, and its shadow formula is internally inconsistent, invalidating the EHT-based constraints.

Reference graph

Works this paper leans on

157 extracted references · 24 canonical work pages · cited by 2 Pith papers

  1. [42]

    Quest for realistic non-singular black-hole geometries: regular-center type,

    H. Maeda, “Quest for realistic non-singular black-hole geometries: regular-center type,” JHEP11, 108 (2022)

    2022

  2. [1]

    K. A. Bronnikov, [arXiv:2211.00743 [gr-qc]]

    arXiv

  3. [2]

    Regular Black Holes: A Short Topic Review,

    C. Lan, H. Yang, Y. Guo and Y. G. Miao, “Regular Black Holes: A Short Topic Review,” Int. J. Theor. Phys. 62, no.9, 202 (2023)

    2023

  4. [3]

    Non-singular general-relativistic gravitational collapse,

    J. M. Bardeen “Non-singular general-relativistic gravitational collapse,” in Proceedings of GR5, Tbil- isi, U.S.S.R, p.174 (1968)

    1968

  5. [4]

    Vacuum nonsingular black hole,

    I. Dymnikova, “Vacuum nonsingular black hole,” Gen. Rel. Grav.24, 235-242 (1992)

    1992

  6. [5]

    Regular black hole in general relativity coupled to nonlinear electro- dynamics,

    E. Ayon-Beato and A. Garcia, “Regular black hole in general relativity coupled to nonlinear electro- dynamics,” Phys. Rev. Lett.80, 5056 (1998). 12

    1998

  7. [6]

    Nonsingular charged black hole solution for nonlinear source,

    E. Ayon-Beato and A. Garcia, “Nonsingular charged black hole solution for nonlinear source,” Gen. Rel. Grav. 31, 629-633 (1999)

    1999

  8. [7]

    New regular black hole solution from nonlinear electrodynamics,

    E. Ayon-Beato and A. Garcia, “New regular black hole solution from nonlinear electrodynamics,” Phys. Lett. B464, 25 (1999)

    1999

Show all 157 references
  1. [8]

    Regular magnetic black holes and monopoles from nonlinear electrodynamics,

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

    2001

  2. [9]

    Regular electrically charged structures in nonlinear electrodynamics coupled to gen- eral relativity,

    I. Dymnikova, “Regular electrically charged structures in nonlinear electrodynamics coupled to gen- eral relativity,” Class. Quant. Grav.21, 4417-4429 (2004)

    2004

  3. [10]

    Four parametric regular black hole solution,

    E. Ayon-Beato and A. Garcia, “Four parametric regular black hole solution,” Gen. Rel. Grav.37, 635 (2005)

    2005

  4. [11]

    Formation and evaporation of regular black holes,

    S. A. Hayward, “Formation and evaporation of regular black holes,” Phys. Rev. Lett.96, 031103 (2006)

    2006

  5. [12]

    Noncommutative geometry inspired Schwarzschild black hole,

    P. Nicolini, A. Smailagic and E. Spallucci, “Noncommutative geometry inspired Schwarzschild black hole,” Phys. Lett. B632, 547-551 (2006)

    2006

  6. [13]

    On a regular modified Schwarzschild spacetime,

    H. Culetu, “On a regular modified Schwarzschild spacetime,” [arXiv:1305.5964 [gr-qc]]

    arXiv

  7. [14]

    Regular black hole metrics and the weak energy condition,

    L. Balart and E. C. Vagenas, “Regular black hole metrics and the weak energy condition,” Phys. Lett. B 730, 14 (2014)

    2014

  8. [15]

    Regular black holes with a nonlinear electrodynamics source,

    L. Balart and E. C. Vagenas, “Regular black holes with a nonlinear electrodynamics source,” Phys. Rev. D 90, no. 12, 124045 (2014)

    2014

  9. [16]

    Magnetically charged regular black hole in a model of nonlinear electrodynamics,

    M. S. Ma, “Magnetically charged regular black hole in a model of nonlinear electrodynamics,” Annals Phys. 362, 529-537 (2015)

    2015

  10. [17]

    Notes on nonsingular models of black holes,

    V. P. Frolov, “Notes on nonsingular models of black holes,” Phys. Rev. D94, no.10, 104056 (2016)

    2016

  11. [18]

    Construction of Regular Black Holes in General Relativity,

    Z. Y. Fan and X. Wang, “Construction of Regular Black Holes in General Relativity,” Phys. Rev. D 94, no.12, 124027 (2016)

    2016

  12. [19]

    Using dominant and weak energy conditions for build new classe of regular black holes,

    M. E. Rodrigues, E. L. B. Junior and M. V. de Sousa Silva, “Using dominant and weak energy conditions for build new classe of regular black holes,” JCAP02, 059 (2018)

    2018

  13. [20]

    Regular multihorizon black holes in General Relativity,

    M. E. Rodrigues, M. V. de Sousa Silva and A. S. de Siqueira, “Regular multihorizon black holes in General Relativity,” Phys. Rev. D102, no.8, 084038 (2020)

    2020

  14. [21]

    Regular model of magnetized black hole with rational nonlinear electrodynamics,

    S. I. Kruglov, “Regular model of magnetized black hole with rational nonlinear electrodynamics,” Int. J. Mod. Phys. A36, no.21, 2150158 (2021)

    2021

  15. [22]

    Black hole as a magnetic monopole within exponential nonlinear electrodynamics,

    S. I. Kruglov, “Black hole as a magnetic monopole within exponential nonlinear electrodynamics,” Annals Phys. 378, 59-70 (2017)

    2017

  16. [23]

    A regular scale-dependent black hole solution,

    E. Contreras, Á. Rincón, B. Koch and P. Bargueño, “A regular scale-dependent black hole solution,” Int. J. Mod. Phys. D27, no.03, 1850032 (2017)

    2017

  17. [24]

    Regular black holes in Einstein-Gauss-Bonnet gravity,

    S. G. Ghosh, D. V. Singh and S. D. Maharaj, “Regular black holes in Einstein-Gauss-Bonnet gravity,” Phys. Rev. D97, no.10, 104050 (2018)

    2018

  18. [25]

    Note on regular magnetic black hole,

    S. H. Mazharimousavi and M. Halilsoy, “Note on regular magnetic black hole,” Phys. Lett. B796, 123-125 (2019)

    2019

  19. [26]

    Regular black holes in Rainbow Gravity,

    E. L. B. Junior, M. E. Rodrigues and M. V. de Sousa Silva, “Regular black holes in Rainbow Gravity,” Nucl. Phys. B961, 115244 (2020)

    2020

  20. [27]

    Regular black holes with exotic topologies,

    G. Melgarejo, E. Contreras and P. Bargueño, “Regular black holes with exotic topologies,” Phys. Dark Univ. 30, 100709 (2020)

    2020

  21. [28]

    Extended phase space thermodynamics of Bardeen black hole in massive gravity,

    B. K. Singh, R. P. Singh and D. V. Singh, “Extended phase space thermodynamics of Bardeen black hole in massive gravity,” Eur. Phys. J. Plus135, no.10, 862 (2020)

    2020

  22. [29]

    Hayward black holes in Einstein–Gauss–Bonnet gravity,

    A. Kumar, D. V. Singh and S. G. Ghosh, “Hayward black holes in Einstein–Gauss–Bonnet gravity,” Annals Phys. 419, 168214 (2020)

    2020

  23. [30]

    Quasinormal modes and shadows of a new family of Ayón-Beato-García black holes,

    X. C. Cai and Y. G. Miao, “Quasinormal modes and shadows of a new family of Ayón-Beato-García black holes,” Phys. Rev. D103, no.12, 124050 (2021)

    2021

  24. [31]

    P − v criticality, phase structure and extended thermo- dynamics of AdS ABG black holes,

    B. K. Singh, R. P. Singh and D. V. Singh, “P − v criticality, phase structure and extended thermo- dynamics of AdS ABG black holes,” Eur. Phys. J. Plus136, no.5, 575 (2021) 13

    2021

  25. [32]

    RemarksonNonsingularModelsofHaywardandMagnetizedBlackHolewithRational Nonlinear Electrodynamics,

    S.I.Kruglov, “RemarksonNonsingularModelsofHaywardandMagnetizedBlackHolewithRational Nonlinear Electrodynamics,” Grav. Cosmol.27, no.1, 78-84 (2021)

    2021

  26. [33]

    Complexity conjecture of regular electric black holes,

    B. B. Asl, S. H. Hendi and S. N. Sajadi, “Complexity conjecture of regular electric black holes,” Phys. Rev. D104, no.10, 104034 (2021)

    2021

  27. [34]

    Exact nonsingular black holes and thermodynamics,

    D. V. Singh, S. G. Ghosh and S. D. Maharaj, “Exact nonsingular black holes and thermodynamics,” Nucl. Phys. B981, 115854 (2022)

    2022

  28. [35]

    Exact solution of Bardeen black hole in Einstein–Gauss–Bonnet gravity,

    A. Kumar, D. V. Singh, Y. Myrzakulov, G. Yergaliyeva and S. Upadhyay, “Exact solution of Bardeen black hole in Einstein–Gauss–Bonnet gravity,” Eur. Phys. J. Plus138, no.12, 1071 (2023)

    2023

  29. [36]

    Electrically charged regular black holes in nonlinear electrodynamics: Light rings, shadows, and gravitational lensing,

    M. A. A. de Paula, H. C. D. Lima, Junior, P. V. P. Cunha and L. C. B. Crispino, “Electrically charged regular black holes in nonlinear electrodynamics: Light rings, shadows, and gravitational lensing,” Phys. Rev. D108, no.8, 084029 (2023)

    2023

  30. [37]

    Regular Charged Black Holes, Energy Conditions, and Quasinormal Modes,

    L. Balart, G. Panotopoulos and Á. Rincón, “Regular Charged Black Holes, Energy Conditions, and Quasinormal Modes,” Fortsch. Phys.71, no.12, 2300075 (2023)

    2023

  31. [38]

    Quasinormal modes of renormalization group improved Dymnikova regular black holes,

    R. A. Konoplya, Z. Stuchlik, A. Zhidenko and A. F. Zinhailo, “Quasinormal modes of renormalization group improved Dymnikova regular black holes,” Phys. Rev. D107, no.10, 104050 (2023)

    2023

  32. [39]

    Bardeen spacetime as a quantum corrected Schwarzschild black hole: Quasinormal modes and Hawking radiation,

    R. A. Konoplya, D. Ovchinnikov and B. Ahmedov, “Bardeen spacetime as a quantum corrected Schwarzschild black hole: Quasinormal modes and Hawking radiation,” Phys. Rev. D108, no.10, 104054 (2023)

    2023

  33. [40]

    Recovery of consistency in thermodynamics of regular black holes in Einstein’s gravity coupled with nonlinear electrodynamics,

    Y. Guo, H. Xie and Y. G. Miao, “Recovery of consistency in thermodynamics of regular black holes in Einstein’s gravity coupled with nonlinear electrodynamics,” Nucl. Phys. B1000, 116491 (2024)

    2024

  34. [41]

    Shadow and greybody bounding of a regular scale-dependent black hole solution,

    A. Övgün, R. C. Pantig and Á. Rincón, “Shadow and greybody bounding of a regular scale-dependent black hole solution,” Annals Phys.463, 169625 (2024)

    2024

  35. [43]

    Stability properties of black holes in selfgravitating nonlinear electro- dynamics,

    C. Moreno and O. Sarbach, “Stability properties of black holes in selfgravitating nonlinear electro- dynamics,” Phys. Rev. D67, 024028 (2003)

    2003

  36. [44]

    New type of regular black holes and particle - like solutions from NED,

    A. Burinskii and S. R. Hildebrandt, “New type of regular black holes and particle - like solutions from NED,” Phys. Rev. D65, 104017 (2002)

    2002

  37. [45]

    Regular black holes and energy conditions,

    O. B. Zaslavskii, “Regular black holes and energy conditions,” Phys. Lett. B688, 278-280 (2010)

    2010

  38. [46]

    Constraints on singularity resolution by nonlinear electrodynam- ics,

    A. Bokulić, I. Smolić and T. Jurić, “Constraints on singularity resolution by nonlinear electrodynam- ics,” Phys. Rev. D106, no.6, 064020 (2022)

    2022

  39. [47]

    Lagrangian reverse engineering for regular black holes,

    A. Bokulic, E. Franzin, T. Juric and I. Smolic, “Lagrangian reverse engineering for regular black holes,” Phys. Lett. B854, 138750 (2024)

    2024

  40. [48]

    Causality and energy conditions in nonlinear electrodynamics,

    J. G. Russo and P. K. Townsend, “Causality and energy conditions in nonlinear electrodynamics,” JHEP 06, 191 (2024)

    2024

  41. [49]

    The Large Scale Structure of Space-Time,

    S. W. Hawking and G. F. R. Ellis, “The Large Scale Structure of Space-Time,” Cambridge University Press, 2023

    2023

  42. [50]

    Regular black holes with improved energy conditions and their analogues in fluids*,

    C. Lan, Y. G. Miao and Y. X. Zang, “Regular black holes with improved energy conditions and their analogues in fluids*,” Chin. Phys. C47, no.5, 052001 (2023)

    2023

  43. [51]

    Limiting density of matter as a universal law of nature,

    M. A. Markov, “Limiting density of matter as a universal law of nature,” JETP Lett. 36, 265-267 (1982), Pisma Zh.Eksp.Teor.Fiz. 36, 214-216 (1982)

    1982

  44. [52]

    PROBLEMS OF A PERPETUALLY OSCILLATING UNIVERSE,

    M. A. Markov, “PROBLEMS OF A PERPETUALLY OSCILLATING UNIVERSE,” Annals Phys. 155, 333-357 (1984)

    1984

  45. [53]

    Decoupling Versus Excluded Volume or Return of the Giant Wormholes,

    J. Polchinski, “Decoupling Versus Excluded Volume or Return of the Giant Wormholes,” Nucl. Phys. B 325, 619-630 (1989)

    1989

  46. [54]

    Do Black Holes Exist?,

    V. P. Frolov, “Do Black Holes Exist?,” [arXiv:1411.6981 [hep-th]]

    arXiv

  47. [55]

    Quantum radiation from an evaporating nonsingular black hole,

    V. P. Frolov and A. Zelnikov, “Quantum radiation from an evaporating nonsingular black hole,” Phys. Rev. D95, no.12, 124028 (2017)

    2017

  48. [56]

    Remarks on non-singular black holes,

    V. P. Frolov, “Remarks on non-singular black holes,” EPJ Web Conf.168, 01001 (2018)

    2018

  49. [57]

    Nonpolynomial Lagrangian approach to regular black holes,

    A. Colléaux, S. Chinaglia and S. Zerbini, “Nonpolynomial Lagrangian approach to regular black holes,” Int. J. Mod. Phys. D27, no.03, 1830002 (2018). 14

    2018

  50. [58]

    The regular black hole in four dimensional Born–Infeld gravity,

    C. G. Böhmer and F. Fiorini, “The regular black hole in four dimensional Born–Infeld gravity,” Class. Quant. Grav. 36, no.12, 12LT01 (2019)

    2019

  51. [59]

    Asymptotic magnetically charged non-singular black hole and its thermo- dynamics,

    A. Ali and K. Saifullah, “Asymptotic magnetically charged non-singular black hole and its thermo- dynamics,” Phys. Lett. B792, 276-283 (2019)

    2019

  52. [60]

    Non-Singular Model of Magnetized Black Hole Based on Nonlinear Electrodynamics,

    S. I. Kruglov, “Non-Singular Model of Magnetized Black Hole Based on Nonlinear Electrodynamics,” Universe 5, no.12, 225 (2019)

    2019

  53. [61]

    Two-dimensional black holes in the limiting curvature theory of gravity,

    V. P. Frolov and A. Zelnikov, “Two-dimensional black holes in the limiting curvature theory of gravity,” JHEP 08, 154 (2021)

    2021

  54. [62]

    Limiting curvature models of gravity,

    V. P. Frolov, “Limiting curvature models of gravity,” Nuovo Cim. C45, no.2, 38 (2022)

    2022

  55. [63]

    Spherically symmetric black holes in the limiting curvature theory of gravity,

    V. P. Frolov and A. Zelnikov, “Spherically symmetric black holes in the limiting curvature theory of gravity,” Phys. Rev. D105, no.2, 024041 (2022)

    2022

  56. [64]

    Black holes in the limiting curvature theory of gravity,

    V. P. Frolov, “Black holes in the limiting curvature theory of gravity,” Int. J. Mod. Phys. A37, no.20n21, 2243009 (2022)

    2022

  57. [65]

    Kilometer-scale ultraviolet regulators and astrophysical black holes,

    J. Boos and C. D. Carone, “Kilometer-scale ultraviolet regulators and astrophysical black holes,” [arXiv:2311.16319 [gr-qc]]

    arXiv

  58. [66]

    Stability of a Schwarzschild singularity,

    T. Regge and J. A. Wheeler, “Stability of a Schwarzschild singularity,” Phys. Rev.108, 1063-1069 (1957)

    1957

  59. [67]

    Effective potential for even parity Regge-Wheeler gravitational perturbation equations,

    F. J. Zerilli, “Effective potential for even parity Regge-Wheeler gravitational perturbation equations,” Phys. Rev. Lett.24, 737-738 (1970)

    1970

  60. [68]

    Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics,

    F. J. Zerilli, “Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics,” Phys. Rev. D2, 2141-2160 (1970)

    1970

  61. [69]

    Perturbation analysis for gravitational and electromagnetic radiation in a reissner- nordstroem geometry,

    F. J. Zerilli, “Perturbation analysis for gravitational and electromagnetic radiation in a reissner- nordstroem geometry,” Phys. Rev. D9, 860-868 (1974)

    1974

  62. [70]

    Gauge-invariant perturbations of Reissner-Nordstrom black holes,

    V. Moncrief, “Gauge-invariant perturbations of Reissner-Nordstrom black holes,” Phys. Rev. D12, 1526-1537 (1975)

    1975

  63. [71]

    Rotating black holes - separable wave equations for gravitational and electromag- netic perturbations,

    S. A. Teukolsky, “Rotating black holes - separable wave equations for gravitational and electromag- netic perturbations,” Phys. Rev. Lett.29, 1114-1118 (1972)

    1972

  64. [72]

    The mathematical theory of black holes,

    S. Chandrasekhar, “The mathematical theory of black holes,” OXFORD, UK: CLARENDON (1985) 646 P

    1985

  65. [73]

    B. P. Abbott et al. [LIGO Scientific and Virgo Collaborations], Phys. Rev. Lett.116 (2016) no.6, 061102 [arXiv:1602.03837 [gr-qc]]

    2016 arXiv

  66. [74]

    https://eventhorizontelescope.org

  67. [75]

    Akiyama et al

    K. Akiyama et al. [Event Horizon Telescope Collaboration], Astrophys. J.875 (2019) no.1, L1

    2019

  68. [76]

    Akiyama et al

    K. Akiyama et al. [Event Horizon Telescope Collaboration], Astrophys. J.875 (2019) no.1, L2

    2019

  69. [77]

    Akiyama et al

    K. Akiyama et al. [Event Horizon Telescope Collaboration], Astrophys. J.875 (2019) no.1, L3

    2019

  70. [78]

    Akiyama et al

    K. Akiyama et al. [Event Horizon Telescope Collaboration], Astrophys. J.875 (2019) no.1, L4

    2019

  71. [79]

    Akiyama et al

    K. Akiyama et al. [Event Horizon Telescope Collaboration], Astrophys. J.875 (2019) no.1, L5

    2019

  72. [80]

    Akiyama et al

    K. Akiyama et al. [Event Horizon Telescope Collaboration], Astrophys. J.875 (2019) no.1, L6

    2019

  73. [81]

    A. E. Broderick, T. Johannsen, A. Loeb and D. Psaltis, Astrophys. J.784 (2014) 7 [arXiv:1311.5564 [astro-ph.HE]]

    2014 arXiv

  74. [82]

    P. G. Nedkova, V. K. Tinchev and S. S. Yazadjiev, Phys. Rev. D 88 (2013) no.12, 124019 [arXiv:1307.7647 [gr-qc]]

    2013 arXiv

  75. [83]

    F. H. Vincent, Z. Meliani, P. Grandclement, E. Gourgoulhon and O. Straub, Class. Quant. Grav.33 (2016) no.10, 105015 [arXiv:1510.04170 [gr-qc]]

    2016 arXiv

  76. [84]

    Ohgami and N

    T. Ohgami and N. Sakai, Phys. Rev. D91 (2015) no.12, 124020 [arXiv:1704.07065 [gr-qc]]

    2015 arXiv

  77. [85]

    Ohgami and N

    T. Ohgami and N. Sakai, Phys. Rev. D94 (2016) no.6, 064071 [arXiv:1704.07093 [gr-qc]]

    2016 arXiv

  78. [86]

    Gyulchev, P

    G. Gyulchev, P. Nedkova, V. Tinchev and S. Yazadjiev, Eur. Phys. J. C 78 (2018) no.7, 544 [arXiv:1805.11591 [gr-qc]]

    2018 arXiv

  79. [87]

    A. B. Abdikamalov, A. A. Abdujabbarov, D. Ayzenberg, D. Malafarina, C. Bambi and B. Ahmedov, Phys. Rev. D100, 024014 (2019) [ arXiv:1904.06207 [gr-qc]. ] 15

    2019 arXiv

  80. [88]

    Shaikh, Phys

    R. Shaikh, Phys. Rev. D98, 024044 (2018)

    2018

  81. [89]

    Shaikh, P

    R. Shaikh, P. Kocherlakota, R. Narayan, and P. S. Joshi, Mon. Not. R. Astron. Soc.482, 52 (2019)

    2019

  82. [90]

    K. S. Virbhadra and G. F. R. Ellis, Phys.Rev. D62,084003 (2000)

    2000

  83. [91]

    K. S. Virbhadra and G. F. R. Ellis, Phys.Rev. D65, 103004 (2002)

    2002

  84. [92]

    P. V. P. Cunha and C. A. R. Herdeiro, Gen. Rel. Grav.50 (2018) no.4, 42 [arXiv:1801.00860 [gr-qc]]

    2018 arXiv

  85. [93]

    J. L. Synge, Mon. Not. Roy. Astron. Soc.131 (1966) no.3, 463

    1966

  86. [94]

    Luminet, Astron

    J.-P. Luminet, Astron. Astrophys.75 (1979) 228

    1979

  87. [95]

    J. M. Bardeen, inBlack Holes (Les Astres Occlus), edited by C. Dewitt and B. S. Dewitt (Gordon and Breach, New York, 1973), pp. 215-239

    1973

  88. [96]

    P. V. P. Cunha, C. A. R. Herdeiro, E. Radu and H. F. Runarsson, Phys. Rev. Lett.115 (2015) no.21, 211102 [arXiv:1509.00021 [gr-qc]]

    2015 arXiv

  89. [97]

    P. V. P. Cunha, C. A. R. Herdeiro, E. Radu and H. F. Runarsson, Int. J. Mod. Phys. D25 (2016) no.09, 1641021 [arXiv:1605.08293 [gr-qc]]

    2016 arXiv

  90. [98]

    Bambi and K

    C. Bambi and K. Freese, Phys. Rev. D79, 043002 (2009) [arXiv:0812.1328 [astro-ph]]

    2009 arXiv

  91. [99]

    Bambi and N

    C. Bambi and N. Yoshida, Class. Quant. Grav.27, 205006 (2010) [arXiv:1004.3149 [gr-qc]]

    2010 arXiv

  92. [100]

    Abdujabbarov, F

    A. Abdujabbarov, F. Atamurotov, Y. Kucukakca, B. Ahmedov and U. Camci, Astrophys. Space Sci. 344 (2013) 429 [arXiv:1212.4949 [physics.gen-ph]]

    2013 arXiv

  93. [101]

    Atamurotov, A

    F. Atamurotov, A. Abdujabbarov and B. Ahmedov, Astrophys. Space Sci.348 (2013) 179

    2013

  94. [102]

    J. W. Moffat, Eur. Phys. J. C75 (2015) no.3, 130 [arXiv:1502.01677 [gr-qc]]

    2015 arXiv

  95. [103]

    Abdujabbarov, B

    A. Abdujabbarov, B. Toshmatov, Z. Stuchlík and B. Ahmedov, Int. J. Mod. Phys. D26 (2016) no.06, 1750051 [arXiv:1512.05206 [gr-qc]]

    2016 arXiv

  96. [104]

    Younsi, A

    Z. Younsi, A. Zhidenko, L. Rezzolla, R. Konoplya and Y. Mizuno, Phys. Rev. D94 (2016) no.8, 084025 [arXiv:1607.05767 [gr-qc]]

    2016 arXiv

  97. [105]

    Schee and Z

    J. Schee and Z. Stuchlik, Eur. Phys. J. C76 (2016) no.11, 643 doi:10.1140/epjc/s10052-016-4511-0

    2016 doi

  98. [106]

    P. V. P. Cunha, C. A. R. Herdeiro, B. Kleihaus, J. Kunz and E. Radu, Phys. Lett. B768 (2017) 373 [arXiv:1701.00079 [gr-qc]]

    2017 arXiv

  99. [107]

    M. Wang, S. Chen and J. Jing, JCAP1710 (2017) no.10, 051 [arXiv:1707.09451 [gr-qc]]

    2017 arXiv

  100. [108]

    Schee, Z

    J. Schee, Z. Stuchlík, B. Ahmedov, A. Abdujabbarov and B. Toshmatov, Int. J. Mod. Phys. D26 (2017) no.5, 1741011

    2017

  101. [109]

    H. M. Wang, Y. M. Xu and S. W. Wei, JCAP1903 (2019) no.03, 046 [arXiv:1810.12767 [gr-qc]]

    2019 arXiv

  102. [110]

    Toshmatov, Z

    B. Toshmatov, Z. Stuchlík, and B. Ahmedov Phys. Rev. D95, 084037 (2017)

    2017

  103. [111]

    R. A. Konoplya, Phys. Lett. B795, 19 (2019)

    2019

  104. [112]

    Khumar and S

    R. Khumar and S. Ghosh, Astrophys. J.892, 78 (2020), arXiv:1811.01260

    2020 arXiv

  105. [113]

    Övgün, I

    A. Övgün, I. Sakalli and J. Saavedra, JCAP10, 041 (2018)

    2018

  106. [114]

    Mishra, S

    A. Mishra, S. Chakraborty, S. Sarkar, Phys. Rev. D99, 104080 (2019) [arXiv:1903.06376 [gr–qc]]

    2019 arXiv

  107. [115]

    Shakih, Phys

    R. Shakih, Phys. Rev. D100, 024028 (2019), arXiv:1904.08322

    2019 arXiv

  108. [116]

    Contreras, J.M Ramirez–VElasquez, Á

    E. Contreras, J.M Ramirez–VElasquez, Á. Rincón, G. Panotopoulos, P. Bargueño, Eur. Phys. J. C 79, 802 (2019). [arXiv:1905.11443]

    2019 arXiv

  109. [117]

    Amir, arXiv: 1906.04146

    Md Sabir Ali and M. Amir, arXiv: 1906.04146

    1906 arXiv

  110. [118]

    Vagnozzi, L

    S. Vagnozzi, L. Visinelli , Phys. Rev. D100 (2019) 024020, [arXiv:1905.12421]

    2019 arXiv

  111. [119]

    Bambi, K

    C. Bambi, K. Freese, S. Vagnozzi, L. Visinelli, Phys. Rev. D100 (2019) 044057 [arXiv:1904.12983]

    2019 arXiv

  112. [120]

    R. A. Konoplya, Phys. Lett. B804 (2020), 135363 [arXiv:1912.10582 [gr-qc]]

    2020 arXiv

  113. [121]

    R. A. Konoplya, T. Pappas and A. Zhidenko, Phys. Rev. D 101 (2020) no.4, 044054 [arXiv:1907.10112 [gr-qc]]

    2020 arXiv

  114. [122]

    Allahyari, M

    A. Allahyari, M. Khodadi, S. Vagnozzi and D. F. Mota, JCAP02 (2020), 003 [arXiv:1912.08231 [gr-qc]]

    2020 arXiv

  115. [123]

    V. K. Tinchev, [arXiv:1911.13262 [gr-qc]]. 16

    1911 arXiv

  116. [124]

    P. V. P. Cunha, C. A. R. Herdeiro and E. Radu, Universe5 (2019) no.12, 220 [arXiv:1909.08039 [gr-qc]]

    2019 arXiv

  117. [125]

    A.Övgün, İ.Sakallı, J.SaavedraandC.Leiva, Mod.Phys.Lett.A 2050163, 2020[arXiv:1906.05954 [hep-th]]

    2020 arXiv

  118. [126]

    R. A. Konoplya and A. Zhidenko, Phys. Rev. D100 (2019) no.4, 044015 [arXiv:1907.05551 [gr-qc]]

    2019 arXiv

  119. [127]

    Hensh, A

    S. Hensh, A. Abdujabbarov, J. Schee and Z. Stuchlík, Eur. Phys. J. C 79 (2019) no.6, 533 [arXiv:1904.08776 [gr-qc]]

    2019 arXiv

  120. [128]

    Stuchlík and J

    Z. Stuchlík and J. Schee, Eur. Phys. J. C79 (2019) no.1, 44

    2019

  121. [129]

    Contreras, Á

    E. Contreras, Á. Rincón, G. Panotopoulos, P. Bargueño and B. Koch, Phys. Rev. D101 (2020) no.6, 064053 [arXiv:1906.06990 [gr-qc]]

    2020 arXiv

  122. [130]

    Fathi, Á

    M. Fathi, Á. Rincón and J. R. Villanueva, Class. Quant. Grav. 37 (2020) no.7, 075004, [arXiv:1903.09037 [gr-qc]]

    2020 arXiv

  123. [131]

    Chang and Q

    Z. Chang and Q. H. Zhu, [arXiv:2006.00685 [gr-qc]]. Shadow of a black hole surrounded by dark matter

    2006 arXiv

  124. [132]

    Badía and E

    J. Badía and E. F. Eiroa, Phys. Rev. D102 (2020) no.2, 024066 [arXiv:2005.03690 [gr-qc]]

    2020 arXiv

  125. [133]

    P. C. Li, M. Guo and B. Chen, Phys. Rev. D101 (2020) no.8, 084041 [arXiv:2001.04231 [gr-qc]]

    2020 arXiv

  126. [134]

    C. Li, S. F. Yan, L. Xue, X. Ren, Y. F. Cai, D. A. Easson, Y. F. Yuan and H. Zhao, Phys. Rev. Res. 2 (2020), 023164 [arXiv:1912.12629 [astro-ph.CO]]

    2020 arXiv

  127. [135]

    Khodadi, A

    M. Khodadi, A. Allahyari, S. Vagnozzi and D. F. Mota, [arXiv:2005.05992 [gr-qc]]

    2005 arXiv

  128. [136]

    Övgün and İ

    A. Övgün and İ. Sakalli, [arXiv:2005.00982 [gr-qc]]

    2005 arXiv

  129. [137]

    C. Liu, T. Zhu, Q. Wu, K. Jusufi, M. Jamil, M. Azreg-Aïnou and A. Wang, Phys. Rev. D101 (2020) no.8, 084001 [arXiv:2003.00477 [gr-qc]]

    2020 arXiv

  130. [138]

    Vagnozzi, C

    S. Vagnozzi, C. Bambi and L. Visinelli, Class. Quant. Grav. 37 (2020) no.8, 087001 [arXiv:2001.02986 [gr-qc]]

    2020 arXiv

  131. [139]

    S. G. Ghosh, M. Amir and S. D. Maharaj, Nucl. Phys. B957 (2020), 115088 [arXiv:2006.07570 [gr-qc]]

    2020 arXiv

  132. [140]

    Rincon and G

    A. Rincon and G. Gómez, Phys. Dark Univ.46 (2024), 101576 [arXiv:2308.11756 [gr-qc]]

    2024 arXiv

  133. [141]

    Övgün, R

    A. Övgün, R. C. Pantig and Á. Rincón, Eur. Phys. J. Plus138 (2023) no.3, 192 [arXiv:2303.01696 [gr-qc]]

    2023 arXiv

  134. [142]

    Contreras, Á

    E. Contreras, Á. Rincón, G. Panotopoulos and P. Bargueño, Annals Phys.432 (2021), 168567 [arXiv:2010.03734 [gr-qc]]

    2021 arXiv

  135. [143]

    Observational predictions of LQG motivated polymerized black holes and con- straints from Sgr A* and M87*,

    R. Kumar Walia, “Observational predictions of LQG motivated polymerized black holes and con- straints from Sgr A* and M87*,” JCAP03, 029 (2023)

    2023

  136. [144]

    Duality rotations and type D solutions to Einstein equations with nonlinear electromagnetic sources,

    H. Salazar I., A. Garcia D., J. F. Plebanski “Duality rotations and type D solutions to Einstein equations with nonlinear electromagnetic sources,” J. Math. Phys., 28, 2171 (1987)

    1987

  137. [145]

    A regular metric does not ensure the regularity of spacetime,

    M. E. Rodrigues and H. A. Vieira, “A regular metric does not ensure the regularity of spacetime,” Eur. Phys. J. Plus138, no.11, 974 (2023)

    2023

  138. [146]

    Lecture notes on general relativity,

    S. M. Carroll, “Lecture notes on general relativity,” [arXiv:gr-qc/9712019 [gr-qc]]

    arXiv

  139. [147]

    C. K. Qiao and M. Li, Phys. Rev. D106 (2022) no.2, L021501 [arXiv:2204.07297 [gr-qc]]

    2022 arXiv

  140. [148]

    R. A. Konoplya and A. F. Zinhailo, Eur. Phys. J. C80(2020) no.11, 1049 [arXiv:2003.01188 [gr-qc]]

    2020 arXiv

  141. [149]

    Ferrari and L

    V. Ferrari and L. Gualtieri, Gen. Rel. Grav.40, 945-970 (2008) [arXiv:0709.0657 [gr-qc]]

    2008 arXiv

  142. [150]

    R. A. Konoplya and A. Zhidenko, Rev. Mod. Phys.83, 793-836 (2011) [arXiv:1102.4014 [gr-qc]]

    2011 arXiv

  143. [151]

    P. A. González, E. Papantonopoulos, Á. Rincón and Y. Vásquez, Phys. Rev. D106 (2022) no.2, 024050 [arXiv:2205.06079 [gr-qc]]

    2022 arXiv

  144. [152]

    P. A. González, Á. Rincón, J. Saavedra and Y. Vásquez, Phys. Rev. D104 (2021) no.8, 084047 [arXiv:2107.08611 [gr-qc]]

    2021 arXiv

  145. [153]

    Harmark, J

    T. Harmark, J. Natario and R. Schiappa, Adv. Theor. Math. Phys. 14, no.3, 727-794 (2010) [arXiv:0708.0017 [hep-th]]

    2010 arXiv

  146. [154]

    B. F. Schutz and C. M. Will, Astrophys. J. Lett.291, L33-L36 (1985). 17

    1985

  147. [155]

    Iyer and C

    S. Iyer and C. M. Will, Phys. Rev. D35, 3621 (1987)

    1987

  148. [156]

    Geodesic stability, Lyapunov exponents and quasinormal modes,

    V. Cardoso, A. S. Miranda, E. Berti, H. Witek and V. T. Zanchin, “Geodesic stability, Lyapunov exponents and quasinormal modes,” Phys. Rev. D79 (2009) 064016 [arXiv:0812.1806 [hep-th]]

    2009 arXiv

  149. [157]

    Ponglertsakul, P

    S. Ponglertsakul, P. Burikham and L. Tannukij, Eur. Phys. J. C 78, no.7, 584 (2018) [arXiv:1803.09078 [gr-qc]]. 18

    2018 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.