Pith. sign in

REVIEW 1 major objections 5 minor 83 references

Absorption spectrum and greybody factors of charged black holes in loop quantum gravity

T0 review · 1 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read A charged loop-quantum-gravity black hole absorbs more scalar radiation as its quantum parameter grows, and less as its charge-to-mass ratio grows.

desk verdict A competent first computation of scalar absorption for the charged LQG black hole, but the b0-vs-M parameterization is ambiguous enough that the headline trend needs a clearer statement. read the letter →

arxiv 2608.05292 v1 pith:RYKG2ZUP submitted 2026-08-05 gr-qc

Marco A. A. de Paula , Valdir B. Bezerra , Luiz C. S. Leite This is my paper · ORCID
classification gr-qc MSC 83C5783C4781T20 PACS 04.70.-s04.62.+v
keywords absorptioncrosssectiongreybodyfactorsloopquantumgravityblackholesscalarwavesReissner-Nordströmcomparisoneffectivepotentialbounceradiuspartial-wavemethod
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 aims to establish that the charged, singularity-free black hole spacetime of loop quantum gravity has a calculable and distinctive absorption spectrum for massless scalar waves. Using the partially polymerized metric, the authors solve the Klein-Gordon equation numerically and compute the total absorption cross section over a wide frequency range. Their central finding is that increasing the quantum parameter $b_0$ raises the total cross section at intermediate frequencies, and the curve with the highest peaks also has the deepest troughs, while increasing the charge-to-mass ratio $Q/M$ lowers the cross section. They also show that greybody factors for higher multipoles can be either enhanced or suppressed by $b_0$ depending on frequency. The interest is that this gives a concrete wave-scattering signature of loop quantum gravity that differs from the classical Reissner-Nordström black hole.

What carries the argument

The central object is the charged loop-quantum-gravity black hole line element built from the Reissner-Nordström function $f(r)$ and a holonomy-corrected radial component controlled by the quantum parameter $b_0 = \sqrt{1+\gamma^2\delta_b^2}$; the classical singularity is replaced by a bounce radius $r_0$ that lies inside the event horizon. The argument is carried by the radial Klein-Gordon equation in the tortoise coordinate, whose effective potential $V(r)$ determines transmission, and by the partial-wave sum $\sigma = \sum_l (\pi/\omega^2)(2l+1)|T_{\omega l}|^2$ for the total absorption cross section. The quantum parameter enters only through the potential and shifts the barrier height, while the charge enters through $f(r)$. Semiclassical checks use the geodesic capture cross section and the high-frequency sinc approximation.

What would settle it

A direct numerical recomputation of the total absorption cross section for the same metric with the bounce radius fixed by a different area-gap identification, or with Eq. (26) dropped altogether, would settle the claim: if the intermediate-frequency growth with $b_0$ and the peak-and-trough anti-correlation disappear, those signatures come from the chosen identification rather than from loop quantum gravity itself.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the charged loop-quantum-gravity black hole is not spectrally identical to Reissner-Nordström even though it shares the same horizons and shadow radius. For massless scalar waves, the quantum parameter $b_0 > 1$ lowers the effective potential barrier, so more of the incident wave tunnels into the black hole; consequently the total absorption cross section grows with $b_0$ from the low-frequency regime up to moderate frequencies, while remaining pinned to the same black-hole area at low frequency and the same geometric capture cross section at high frequency. The numerical spectra also show an anti-correlation between peaks and troughs as $b_0$ varies: the configuration with the largest peaks has the deepest troughs. Increasing $Q/M$, by contrast, raises the barrier and suppresses absorption at all frequencies. The greybody-factor calculation shows the same two trends, with the $l \geq 1$ partial waves reversing the $b_0$ effect in some frequency windows.

Load-bearing premise

The paper assumes that the interior bounce surface has exactly the smallest area loop quantum gravity allows, and that this fixes the quantum parameter; if that identification or the analytic continuation to the exterior metric is wrong, the reported absorption pattern would not describe real quantum black holes.

Editorial extensions

If this is right

  • In the low-frequency and high-frequency limits, the total absorption cross section matches the horizon area and the geometric capture cross section, so quantum effects are invisible in those regimes.
  • In the intermediate range, a larger $b_0$ makes the black hole a stronger absorber of scalar radiation, and the peak-and-trough anti-correlation provides a quantitative signature to look for.
  • Because the shadow radius is identical to Reissner-Nordström, shadow-imaging experiments cannot distinguish the two spacetimes; the absorption spectrum is one of the few observables that can.
  • Higher charge-to-mass ratio suppresses absorption, so the most promising loop-quantum-gravity signature appears for low-charge configurations with $b_0$ as large as allowed.
  • The greybody factors determine particle emission rates, so the $b_0$-dependence found here should show up in the evaporation spectrum if this metric is the correct effective description.

Reading between the lines

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

  • A natural next check is whether the same peak-and-trough anti-correlation appears for electromagnetic and gravitational perturbations, since those are the fields with the most direct astrophysical emission spectra.
  • The charge bound derived from the area-gap identification is scale-dependent in Planck units, so for very massive astrophysical black holes the allowed charge-to-mass ratio is strongly suppressed; the predicted absorption signature is therefore most relevant for small, near-extremal remnants.
  • Computing the scattering cross section, not just absorption, should reveal the same anti-correlation as complementary interference patterns, since the same partial-wave transmission coefficients control both.
  • Repeating the calculation in other loop-quantum-gravity-inspired regular black hole models would separate features universal to the bounce from features specific to the uniparametric polymerization scheme used here.
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

1 major / 5 minor

Summary. The paper computes absorption cross sections and greybody factors for massless scalar fields on the charged loop quantum gravity black hole spacetime of Ref. [20], obtained through the uniparametric polymerization scheme. After reviewing the metric (Eq. 24) and its properties (bounce radius, charge bounds, effective potential), the authors numerically solve the Klein-Gordon equation and present partial and total absorption cross sections for various values of the quantum parameter b0 and the charge-to-mass ratio Q/M. The main reported findings are that, for fixed Q/M, increasing b0 enhances the total ACS in the intermediate frequency range, with the highest-peak curve also showing the deepest troughs, while increasing Q/M decreases the ACS. The numerical results are benchmarked against the low-frequency area limit, the geodesic capture cross section, and the sinc approximation, and RN mimic configurations are discussed.

Significance. This is the first detailed absorption analysis for this LQG-inspired charged black hole, and it contains potentially interesting imprints of the quantum parameter in the intermediate-frequency interference pattern. The numerical method is standard and the consistency checks against known limits (low-frequency horizon area, high-frequency geodesic and sinc behaviour) are a genuine strength; these benchmarks are external to the LQG model and do not rely on fitting the target cross sections. The effective-potential explanation of the Q/M trend is also convincing. However, the significance of the central b0-trend is reduced by the unresolved status of the area-gap identification: the manuscript never states whether b0 is a free parameter in the numerical scans or is fixed by Eq. (27) as a function of M and Q. Until that is clarified, the domain of the headline claim is ambiguous. If the ambiguity is resolved, the paper would be a solid contribution to LQG black-hole phenomenology.

major comments (1)
  1. [Sec. II B (Eqs. 26–28) vs. Sec. V C (Figs. 10, 13, 14)]
minor comments (5)
  1. [Sec. IV B, Eq. (56)] The expression for X in the analytical greybody bound is presented without derivation; since this is not a standard textbook result, the authors should either provide the intermediate steps or cite the source where the bound is computed.
  2. [Sec. V A] The numerical integration accuracy is not discussed; a brief convergence check (e.g., varying the outer boundary r_inf = 10^3 M and the step size) would strengthen the reported agreement with the known analytical limits.
  3. [Sec. V C, figure captions] The captions of Figs. 10, 13 and 14 should state the mass convention used in the parameter scans (e.g., whether M is set to 1) and whether the area-gap relation (27) is imposed; this would remove the ambiguity discussed in the major comment.
  4. [Sec. II B, Eq. (28) and footnote 2] The footnote about the dimensionality of the charge bound is useful, but the scale dependence (mass in Planck units) should be discussed in the main text, since it determines whether the high-charge-to-mass regimes used in the absorption plots are physically realizable for astrophysical black holes.
  5. [Sec. V B] There are several typographical issues, including 'the fundamental model= 0' (presumably 'mode l=0') and missing articles; a thorough proofreading pass is recommended.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the absorption cross sections are obtained by solving the Klein-Gordon equation and are benchmarked against independent Reissner-Nordstrom, Schwarzschild, geodesic, and sinc-approximation limits; the only flagged limitations are a parameter-domain ambiguity involving Eq.

full rationale

The central claim, that the total ACS increases with the quantum parameter b0 at fixed Q/M and decreases with Q/M at fixed b0, is derived by numerically integrating the radial Klein-Gordon equation (46) with the metric of Eq. (24) and the boundary conditions of Eq. (48); no absorption quantity is fitted to the target cross sections. The numerical code is validated against independent external benchmarks: the low-frequency limit matches the horizon area (Eq. (59), "the ACS matches the BH area for low-frequency massless scalar waves, as expected [78]"), the oscillations are reproduced by the sinc approximation (41), and the b0=1 limit recovers the RN/Schwarzschild geometry. The analytical greybody bound of Eqs. (53)-(56) is derived from the effective potential rather than from the numerics, and Fig. 8 explicitly shows it disagrees with the numerics outside the low-frequency range, so it is not used to force the reported behavior. The mimic-setup statement in Sec. V D is a direct consequence of the shared metric function f(r) and is not an imported prediction. The g_tt component is not re-derived in full: the text states "performing the appropriate analytical continuation as derived and detailed in Refs. [20,21]" (Sec. II B); this is an omitted proof in the present work, but Refs. [20,21] are not by the present authors, so the deferred result is independent support rather than a circular chain. Several references are self-citations (e.g., Refs. [47], [53]-[56], [80]), but they are used only as methodological background for wave-scattering computations and are not load-bearing for the new results. Two caveats keep the score slightly above zero. First, if the area-gap identification of Eq. (26) is enforced, Eq. (27) makes b0 a function of M and Q, whereas the scans in Sec. V C vary b0 at fixed Q/M without stating whether M is held fixed; this is a parameter-domain ambiguity that could conflate mass dependence with quantum effects, but it does not make the numerical ACS prediction equivalent to the metric input. Second, footnote 2 in Sec. II B explicitly concedes that the extremal-charge bound of Eq. (28) is scale-dependent because M is measured in Planck units; this is a modeling limitation, not a circular step, because the absorption computation does not rely on that bound. No circular step can be exhibited in which a prediction reduces by construction to a fitted parameter or to a self-citation chain.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the charged LQG metric of Ref. [20], which is reviewed but not derived in this paper. The key axioms are the polymerization scheme, the analytic continuation producing the exterior metric, the area-gap identification that fixes the parameter space, and the test-field approximation. No new entities are introduced.

free parameters (2)
  • b0 (quantum parameter) = varied from 1 to 3
    Varies the strength of LQG corrections; treated as an independent parameter in the numerical study, though in the model it is determined by δ_b via b0 = sqrt(1 + gamma^2 delta_b^2).
  • gamma (Barbero-Immirzi parameter) = sqrt(3)/6
    Chosen to match a common LQG value; the paper claims conclusions do not depend on this choice.
assumptions (5)
  • domain assumption The uniparametric polymerization scheme with effective Hamiltonian (Eq. 7) describes the quantum-corrected charged black hole.
    This is the LQG model taken from Refs. [18-20]; the paper reviews it but does not derive it.
  • domain assumption The effective Hamiltonian constraint and analytic continuation (Sec. II B) yield the exterior metric (Eq. 24) with the same horizons as RN.
    The metric is obtained by performing the appropriate analytical continuation as derived and detailed in Refs. [20,21]; assumed valid for all r >= r+.
  • ad hoc to paper The bounce area equals the LQG area gap, 4πr0^2 = 4√3πγ (Eq. 26).
    This condition is imposed to fix δ_b (Eq. 27) and yields the charge bound (Eq. 28); other identifications would change the allowed parameter space.
  • domain assumption The massless scalar field does not backreact on the spacetime and obeys the Klein-Gordon equation (Eq. 43).
    Test-field approximation standard in black hole scattering.
  • domain assumption Numerical solutions are matched to asymptotic plane-wave boundary conditions (Eq. 48) with a purely ingoing wave at the horizon.
    Standard absorption boundary conditions; assumes no reflection at the horizon.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Absorption spectrum and greybody factors of charged black holes in loop quantum gravity." pith.science (2026). https://pith.science/paper/RYKG2ZUP

@misc{pith2026260805292,
  author       = {Pith},
  title        = {Pith review of: Absorption spectrum and greybody factors of charged black holes in loop quantum gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RYKG2ZUP}},
  note         = {Machine review of arXiv:2608.05292}
}
read the original abstract

In the last few decades, singularity-free black holes (BHs) obtained in the framework of Loop Quantum Gravity (LQG) have gained attention in the literature. These compact objects replace the classical singularity with a transition hypersurface called the bounce radius and stand out as potential scenarios for exploring the imprints of LQG in BH physics. Although scalar perturbations in the vicinity of LQG-based BHs are currently being studied, the absorption spectrum has not yet been analyzed in detail. In this work, we present an in-depth investigation of the absorption properties of massless test scalar fields by a charged LQG BH, aiming to better understand the role played by the quantum and charge parameters of the BH spacetime. Using a numerical approach, we compute the absorption cross section (ACS) of the massless scalar wave for arbitrary values of the frequency of the incident wave. We find that the behavior of the ACS as we increase the quantum parameter indicates that the peaks and troughs of the total ACS exhibit opposite behaviors, i.e., the curve related to the highest peak corresponds to the deepest troughs. Moreover, we show that the ACS decreases as we consider higher values of the BH charge-to-mass ratio. This is in stark contrast to the behavior of the absorption spectrum as we vary the quantum parameter. We also draw comparisons with the Reissner-Nordstrom (RN) BH, exploring the situations where LQG and RN BHs can have the same absorption properties. Furthermore, we find excellent agreement between our numerical results and the well-known classical and semiclassical approximations for the total ACS in their corresponding limits. For completeness, we also investigate the greybody factors. Our results can be viewed as a first step toward a better understanding of the absorption properties of LQG-inspired BHs.

Figures

Figures reproduced from arXiv: 2608.05292 by the authors.

Figure 1
Figure 1. FIG. 1. Allowed and disallowed values of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Kretschmann scalar invariant of the charged LQG BH space [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Metric function of the charged BH in LQG, considering [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figures from the paper (9 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Lyapunov exponent of the charged LQG, as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Effective potential of massless scalar waves in the back [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. GBF computed analytically, as a function of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 10
Figure 10. Figure 10: FIG. 10. GBFs of massless scalar waves in the background of the [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Comparison between the total ACS computed numerically [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Comparison between the total and partial ACSs of massless [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Total (top panel) and partial (bottom panel) ACSs of mass [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Total ACS of massless scalar waves in the background of [PITH_FULL_IMAGE:figures/full_fig_p010_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Total ACSs of massless scalar waves in the background of the charged LQG and RN BH spacetimes with [PITH_FULL_IMAGE:figures/full_fig_p012_15.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

83 extracted references · 32 canonical work pages

  1. [20]

    AlonsoBardaji, D

    A. AlonsoBardaji, D. Brizuela, and R. Vera, Nonsingular spher- 13 ically symmetric black-hole model with holonomy corrections, Phys. Rev. D106, 024035 (2022), arXiv:2205.02098

    arXiv 2022

  2. [1]

    regular quantum transition

    Then, by introducing the regularization factor given by cos(δbb)p 1 +γ 2δ2 b ,(6) we can construct an effective Hamiltonian, namely, 1 Notice also that despite their simplicity, scalar fields are also relevant from the astrophysical point of view. They are important in the inflation era [28], can be used to describe dark energy [29, 30], and can be treate...

  3. [2]

    A. J. Kox, M. J. Klein, and R. Schulmann, The collected papers of albert einstein; volume 6 the berlin years: Writings 1914- 1917, European Journal of Physics18, 52 (1997)

    1997

  4. [3]

    R. M. Wald,General relativity(University of Chicago Press, Chicago, United States, 1984)

    1984

  5. [4]

    T. L. S. Collaboration, T. V . Collaboration, and the Kagra Col- laboration, Gwtc-4.0: An introduction to version 4.0 of the gravitational-wave transient catalog, The Astrophysical Journal Letters995(2025)

    work page 2025

  6. [5]

    Akiyamaet al.(Event Horizon Telescope), First M87 Event Horizon Telescope Results

    K. Akiyamaet al.(Event Horizon Telescope), First M87 Event Horizon Telescope Results. I. The Shadow of the Su- permassive Black Hole, Astrophys. J. Lett.875, L1 (2019), arXiv:1906.11238 [astro-ph.GA]

    arXiv 2019

  7. [6]

    Akiyamaet al.(Event Horizon Telescope), First Sagittar- ius A* Event Horizon Telescope Results

    K. Akiyamaet al.(Event Horizon Telescope), First Sagittar- ius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way, Astrophys. J. Lett.930, L12 (2022), arXiv:2311.08680 [astro- ph.HE]

    arXiv 2022

  8. [7]

    Heusler,Black hole uniqueness theorems(Cambridge Uni- versity Press, Cambridge, England, 1996)

    M. Heusler,Black hole uniqueness theorems(Cambridge Uni- versity Press, Cambridge, England, 1996)

    work page 1996

Show all 83 references
  1. [8]

    S. W. Hawking and R. Penrose, The Singularities of gravita- tional collapse and cosmology, Proc. Roy. Soc. Lond. A314, 529 (1970)

    1970

  2. [9]

    S. W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys.43, 199 (1975), [Erratum: Commun.Math.Phys. 46, 206 (1976)]

    1975

  3. [10]

    Ashtekar and J

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

    2004 arXiv

  4. [11]

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

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

    2007

  5. [12]

    Gambini and J

    R. Gambini and J. Pullin,A first course in loop quantum gravity (OUP Oxford, 2011)

    2011

  6. [13]

    Rovelli and F

    C. Rovelli and F. Vidotto,Covariant Loop Quantum Grav- ity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2014)

    2014

  7. [14]

    Corichi and P

    A. Corichi and P. Singh, Loop quantization of the Schwarzschild interior revisited, Class. Quant. Grav.33, 055006 (2016), arXiv:1506.08015

    2016 arXiv

  8. [15]

    Han and H

    M. Han and H. Liu, Covariantµ¯-scheme effective dynam- ics, mimetic gravity, and nonsingular black holes: Applications to spherically symmetric quantum gravity, Phys. Rev. D109, 084033 (2024), arXiv:2212.04605 [gr-qc]

    2024 arXiv

  9. [16]

    Zhang, Loop Quantum Black Hole, Universe9, 313 (2023), arXiv:2308.10184

    X. Zhang, Loop Quantum Black Hole, Universe9, 313 (2023), arXiv:2308.10184

    2023 arXiv

  10. [17]

    Perez, Black Holes in Loop Quantum Gravity, Rept

    A. Perez, Black Holes in Loop Quantum Gravity, Rept. Prog. Phys.80, 126901 (2017), arXiv:1703.09149

    2017 arXiv

  11. [18]

    L.-G. Zhu, G. Fu, S. Li, D. Zhang, and J.-P. Wu, Quasinormal modes of a charged loop quantum black hole, Phys. Rev. D111, 104008 (2025), arXiv:2410.00543 [gr-qc]

    2025 arXiv

  12. [19]

    AlonsoBardaji, D

    A. AlonsoBardaji, D. Brizuela, and R. Vera, An effective model for the quantum Schwarzschild black hole, Phys. Lett. B829, 137075 (2022), arXiv:2112.12110

    2022 arXiv

  13. [21]

    H. A. Borges, I. P. R. Baranov, F. C. Sobrinho, and S. Carneiro, Remnant loop quantum black holes, Class. Quant. Grav.41, 05LT01 (2024), arXiv:2310.01560 [gr-qc]

    2024 arXiv

  14. [22]

    F. C. Sobrinho, H. A. Borges, I. P. R. Baranov, and S. Carneiro, On the horizon area of effective loop quantum black holes, Class. Quant. Grav.40, 145003 (2023), arXiv:2212.11199 [gr- qc]

    2023 arXiv

  15. [23]

    Narayan, Black holes in astrophysics, New J

    R. Narayan, Black holes in astrophysics, New J. Phys.7, 199 (2005), arXiv:gr-qc/0506078

    2005 arXiv

  16. [24]

    E. R. Livine, C. Montagnon, N. Oshita, and H. Roussille, Scalar Quasi-Normal Modes of a loop quantum black hole, JCAP10, 037, arXiv:2405.12671 [gr-qc]

    arXiv

  17. [25]

    S. V . Bolokhov, Long-lived quasinormal modes and overtones’ behavior of holonomy-corrected black holes, Phys. Rev. D110, 024010 (2024), arXiv:2311.05503 [gr-qc]

    2024 arXiv

  18. [26]

    Z. S. Moreira, H. C. D. Lima Junior, L. C. B. Crispino, and C. A. R. Herdeiro, Quasinormal modes of a holonomy corrected Schwarzschild black hole, Phys. Rev. D107, 104016 (2023), arXiv:2302.14722 [gr-qc]

    2023 arXiv

  19. [27]

    D. M. Gingrich, Quasinormal modes of a nonsingular spheri- cally symmetric black hole effective model with holonomy cor- rections, Phys. Rev. D110, 084045 (2024), arXiv:2404.04447 [gr-qc]

    2024 arXiv

  20. [28]

    R. G. Daghigh, M. D. Green, and G. Kunstatter, Scalar Perturbations and Stability of a Loop Quantum Corrected Kruskal Black Hole, Phys. Rev. D103, 084031 (2021), arXiv:2012.13359 [gr-qc]

    2021 arXiv

  21. [29]

    J. E. Lidsey, A. R. Liddle, E. W. Kolb, E. J. Copeland, T. Bar- reiro, and M. Abney, Reconstructing the inflation potential : An overview, Rev. Mod. Phys.69, 373 (1997), arXiv:astro- ph/9508078

    1997

  22. [30]

    P. J. E. Peebles and B. Ratra, The Cosmological Constant and Dark Energy, Rev. Mod. Phys.75, 559 (2003), arXiv:astro- ph/0207347

    2003

  23. [31]

    Padmanabhan, Cosmological constant: The Weight of the vacuum, Phys

    T. Padmanabhan, Cosmological constant: The Weight of the vacuum, Phys. Rept.380, 235 (2003), arXiv:hep-th/0212290

    2003 arXiv

  24. [32]

    Barranco, A

    J. Barranco, A. Bernal, J. C. Degollado, A. Diez-Tejedor, M. Megevand, M. Alcubierre, D. Nunez, and O. Sarbach, Are black holes a serious threat to scalar field dark matter models?, Phys. Rev. D84, 083008 (2011), arXiv:1108.0931 [gr-qc]

    2011 arXiv

  25. [33]

    Futterman, F

    J. Futterman, F. Handler, and R. A. Matzner, Scattering from black holes, Cambridge; New York: Cambridge University Press (1988)

    1988

  26. [34]

    L. C. B. Crispino, A. Higuchi, E. S. Oliveira, and J. V . Rocha, Greybody factors for nonminimally coupled scalar fields in Schwarzschild–de Sitter spacetime, Phys. Rev. D87, 104034 (2013), arXiv:1304.0467 [gr-qc]

    2013 arXiv

  27. [35]

    Heidari, C

    N. Heidari, C. F. B. Macedo, A. A. A. Filho, and H. Hassan- abadi, Scattering effects of bumblebee gravity in metric-affine formalism, Eur. Phys. J. C84, 1221 (2024), arXiv:2407.05321 [gr-qc]

    2024 arXiv

  28. [36]

    W. G. Unruh, Absorption Cross-Section of Small Black Holes, Phys. Rev. D14, 3251 (1976)

    1976

  29. [37]

    Jung and D

    E. Jung and D. K. Park, Effect of scalar mass in the absorp- tion and emission spectra of Schwarzschild black hole, Class. Quant. Grav.21, 3717 (2004), arXiv:hep-th/0403251

    2004 arXiv

  30. [38]

    L. C. B. Crispino, A. Higuchi, and E. S. Oliveira, Electromag- netic absorption cross section of reissner-nordstrom black holes revisited, Phys. Rev. D80, 104026 (2009)

    2009

  31. [39]

    L. C. B. Crispino, S. R. Dolan, and E. S. Oliveira, Scattering of massless scalar waves by Reissner-Nordstr ¨om black holes, Phys. Rev. D79, 064022 (2009), arXiv:0904.0999 [gr-qc]

    2009 arXiv

  32. [40]

    C. L. Benone, E. S. de Oliveira, S. R. Dolan, and L. C. B. Crispino, Absorption of a massive scalar field by a charged black hole, Phys. Rev. D89, 104053 (2014), arXiv:1404.0687 [gr-qc]

    2014 arXiv

  33. [41]

    C. L. Benone and L. C. B. Crispino, Superradiance in static black hole spacetimes, Phys. Rev. D93, 024028 (2016), arXiv:1511.02634 [gr-qc]

    2016 arXiv

  34. [42]

    Delhom, C

    A. Delhom, C. F. B. Macedo, G. J. Olmo, and L. C. B. Crispino, Absorption by black hole remnants in metric-affine gravity, Phys. Rev. D100, 024016 (2019), arXiv:1906.06411 [gr-qc]

    2019 arXiv

  35. [43]

    H. C. D. Lima, C. L. Benone, and L. C. B. Crispino, Scalar absorption: Black holes versus wormholes, Phys. Rev. D101, 124009 (2020), arXiv:2006.03967 [gr-qc]

    2020 arXiv

  36. [44]

    M. A. Anacleto, F. A. Brito, S. J. S. Ferreira, and E. Passos, Ab- sorption and scattering of a black hole with a global monopole in f(r) gravity, Phys. Lett. B788, 231 (2019), arXiv:1701.08147 [hep-th]

    2019 arXiv

  37. [45]

    Huang, J

    H. Huang, J. Chen, Y . Wang, and T. Lu, Absorption of planar waves in conformal gravity spacetime, Gen. Rel. Grav.51, 22 (2019)

    2019

  38. [46]

    Li and Y .-G

    Y . Li and Y .-G. Miao, Absorption cross section of regular black holes in scalar-tensor conformal gravity, Phys. Rev. D105, 044031 (2022), arXiv:2108.06470 [gr-qc]

    2022 arXiv

  39. [47]

    S. V . M. C. B. Xavier, C. L. Benone, and L. C. B. Crispino, Ab- sorption by stringy black holes, Eur. Phys. J. C81, 1127 (2021), arXiv:2112.12865 [gr-qc]

    2021 arXiv

  40. [48]

    C. F. B. Macedo, L. C. S. Leite, and L. C. B. Crispino, Absorp- tion by dirty black holes: null geodesics and scalar waves, Phys. Rev. D93, 024027 (2016), arXiv:1511.08781 [gr-qc]

    2016 arXiv

  41. [49]

    M. A. Anacleto, F. A. Brito, J. A. V . Campos, and E. Passos, Ab- sorption and scattering of a noncommutative black hole, Phys. Lett. B803, 135334 (2020), arXiv:1907.13107 [hep-th]

    2020 arXiv

  42. [50]

    M. A. Anacleto, F. A. Brito, J. A. V . Campos, and E. Passos, Absorption, scattering and shadow by a noncommutative black hole with global monopole, Eur. Phys. J. C83, 298 (2023), arXiv:2212.13973 [hep-th]

    2023 arXiv

  43. [51]

    C. F. B. Macedo and L. C. B. Crispino, Absorption of planar massless scalar waves by Bardeen regular black holes, Phys. Rev. D90, 064001 (2014), arXiv:1408.1779 [gr-qc]

    2014 arXiv

  44. [52]

    P. A. Sanchez, N. Bret´on, and S. E. P. Bergliaffa, Scattering and absorption of massless scalar waves by born–infeld black holes, Annals of Physics393, 107 (2018)

    2018

  45. [53]

    Fernando, Bardeen–de Sitter black holes, Int

    S. Fernando, Bardeen–de Sitter black holes, Int. J. Mod. Phys. D26, 1750071 (2017), arXiv:1611.05337 [gr-qc]

    2017 arXiv

  46. [54]

    M. A. A. Paula, L. C. S. Leite, and L. C. B. Crispino, Electri- cally charged black holes in linear and nonlinear electrodynam- ics: Geodesic analysis and scalar absorption, Phys. Rev. D102, 104033 (2020), arXiv:2011.08633 [gr-qc]

    2020 arXiv

  47. [55]

    M. A. A. de Paula, L. C. S. Leite, and L. C. B. Crispino, Geodesic analysis, absorption and scattering in the static hay- ward spacetime, inTribute to Ruben Aldrovandi, edited by F. Caruso, J. G. Pereira, and A. Santoro (Editora Livraria da F´ısica, S˜ao Paulo, 2024) arXiv:231...

    2024 arXiv

  48. [56]

    Absorption and scattering of massless scalar wave from Regular Black Holes

    M. A. A. de Paula, L. C. dos Santos Leite, and L. C. B. Crispino, Comment on: “Absorption and scattering of massless scalar wave from Regular Black Holes”, Gen. Rel. Grav.55, 73 (2023)

    2023

  49. [57]

    R. B. Magalh ˜aes, L. C. S. Leite, and L. C. B. Crispino, Ab- sorption by deformed black holes, Phys. Lett. B805, 135418 (2020), arXiv:2004.08438 [gr-qc]

    2020 arXiv

  50. [58]

    Heidari, A

    N. Heidari, A. A. Ara ´ujo Filho, R. C. Pantig, and A. ¨Ovg¨un, Absorption, scattering, geodesics, shadows and lensing phe- nomena of black holes in effective quantum gravity, Phys. Dark Univ.47, 101815 (2025), arXiv:2410.08246 [gr-qc]. 14

    2025 arXiv

  51. [59]

    Ashtekar, J

    A. Ashtekar, J. Olmedo, and P. Singh, Quantum extension of the Kruskal spacetime, Phys. Rev. D98, 126003 (2018), arXiv:1806.02406 [gr-qc]

    2018 arXiv

  52. [60]

    Immirzi, Quantum gravity and Regge calculus, Nucl

    G. Immirzi, Quantum gravity and Regge calculus, Nucl. Phys. B Proc. Suppl.57, 65 (1997), arXiv:gr-qc/9701052

    1997 arXiv

  53. [61]

    J. F. Barbero G., Real Ashtekar variables for Lorentzian sig- nature space times, Phys. Rev. D51, 5507 (1995), arXiv:gr- qc/9410014

    1995

  54. [62]

    Gambini, F

    R. Gambini, F. Ben´ıtez, and J. Pullin, A Covariant Polymerized Scalar Field in Semi-Classical Loop Quantum Gravity, Uni- verse8, 526 (2022), arXiv:2102.09501 [gr-qc]

    2022 arXiv

  55. [63]

    Greiner and J

    W. Greiner and J. Reinhardt,Quantum electrodynamics (Springer Science & Business Media, Berlin, Germany, 2013)

    2013

  56. [64]

    Goldstein, C

    H. Goldstein, C. P. Poole, and J. L. Safko,Classical Mechanics, 3rd ed. (Addison-Wesley, San Francisco, United States, 2001)

    2001

  57. [65]

    Modesto, Semiclassical loop quantum black hole, Interna- tional Journal of Theoretical Physics49, 1649 (2010)

    L. Modesto, Semiclassical loop quantum black hole, Interna- tional Journal of Theoretical Physics49, 1649 (2010)

    2010

  58. [66]

    F. S. N. Lobo, M. E. Rodrigues, M. V . de Sousa Silva, A. Simp- son, and M. Visser, Novel black-bounce spacetimes: worm- holes, regularity, energy conditions, and causal structure, Phys. Rev. D103, 084052 (2021), arXiv:2009.12057 [gr-qc]

    2021 arXiv

  59. [67]

    K. A. Bronnikov and S. G. Rubin,Black Holes, Cosmology and Extra Dimensions(World Scientific Publishing Company, Sin- gapore, 2012)

    2012

  60. [68]

    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, 084029 (2023), arXiv:2305.04776 [gr-qc]

    2023 arXiv

  61. [69]

    D´ecanini, G

    Y . D´ecanini, G. Esposito-Far`ese, and A. Folacci, Universality of high-energy absorption cross sections for black holes, Physical Review D83, 10.1103/physrevd.83.044032 (2011)

    2011 doi

  62. [70]

    D´ecanini, A

    Y . D´ecanini, A. Folacci, and B. Raffaelli, Fine structure of high- energy absorption cross sections for black holes, Classical and Quantum Gravity28, 175021 (2011)

    2011

  63. [71]

    Cardoso, A

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

    2009 arXiv

  64. [72]

    Pedrotti and M

    D. Pedrotti and M. Calz `a, Trinity of black hole correspon- dences: Shadows, quasinormal modes, graybody factors, and cautionary remarks, Phys. Rev. D111, 124056 (2025), arXiv:2504.01909 [gr-qc]

    2025 arXiv

  65. [73]

    Boonserm and M

    P. Boonserm and M. Visser, Bounding the greybody factors for Schwarzschild black holes, Phys. Rev. D78, 101502 (2008), arXiv:0806.2209 [gr-qc]

    2008 arXiv

  66. [74]

    Sakalli and S

    ˙I. Sakalli and S. Kanzi, Topical Review: greybody factors and quasinormal modes for black holes in various theories - fingerprints of invisibles, Turk. J. Phys.46, 51 (2022), arXiv:2205.01771 [hep-th]

    2022 arXiv

  67. [75]

    Nakarachinda, S

    R. Nakarachinda, S. Polkong, and P. Wongjun, Greybody factor for massive scalar field in charged black hole, Eur. Phys. J. Plus 140, 838 (2025), arXiv:2501.02247 [gr-qc]

    2025 arXiv

  68. [76]

    Boonserm and M

    P. Boonserm and M. Visser, Bounding the Bogoliubov co- efficients, Annals Phys.323, 2779 (2008), arXiv:0801.0610 [quant-ph]

    2008 arXiv

  69. [77]

    Boonserm,Rigorous bounds on Transmission, Reflec- tion, and Bogoliubov coefficients, Other thesis (2009), arXiv:0907.0045 [math-ph]

    P. Boonserm,Rigorous bounds on Transmission, Reflec- tion, and Bogoliubov coefficients, Other thesis (2009), arXiv:0907.0045 [math-ph]

    2009 arXiv

  70. [78]

    W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flan- nery,Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University Press, Cambridge, England, 2007)

    2007

  71. [79]

    Higuchi, Low-frequency scalar absorption cross sections for stationary black holes, Classical and Quantum Gravity18, L139 (2001)

    A. Higuchi, Low-frequency scalar absorption cross sections for stationary black holes, Classical and Quantum Gravity18, L139 (2001)

    2001

  72. [80]

    J. D. Bekenstein, Extraction of energy and charge from a black hole, Phys. Rev. D7, 949 (1973)

    1973

  73. [81]

    M. A. A. de Paula, L. C. S. Leite, S. R. Dolan, and L. C. B. Crispino, Absorption and unbounded superradiance in a static regular black hole spacetime, Phys. Rev. D109, 064053 (2024), arXiv:2401.01767 [gr-qc]

    2024 arXiv

  74. [82]

    Ashraf, A

    A. Ashraf, A. Ditta, A. Bouzenada, A. Abd-Elmonem, N. S. E. Abdalla, and F. Atamurotov, Thermal fluctuations, particle col- lision, qpos, and emission energy around a schwarzschild black hole immersed in dehnen-type dark matter halo, Physics of the Dark Universe47, 101823 (2025)

    2025

  75. [83]

    Ara ´ujo Filho, A

    A. Ara ´ujo Filho, A. Kumar, N. Heidari, C. Pereira, A. R. Queiroz, and V . Bezerra, A rotating black hole in a hern- quist dark matter halo: horizon geometry, thermodynamics, and quantum emission, arXiv e-prints , arXiv (2026)

    2026

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.