Pith. sign in

REVIEW 4 major objections 4 minor 1 cited by

Spinning Particle Dynamics and ISCO in Covariant Loop Quantum Gravity

T0 review · 4 major / 4 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 Covariant loop-quantum-gravity corrections can erase the innermost stable circular orbit of spinning particles for one effective metric, replacing it with a hovering solution, while the other metric keeps the ISCO but narrows the allowed…

desk verdict A clean MPD-ISCO application to two covariant LQG metrics, but the central 'ISCO disappears' claim is only checked on the V_eff+ branch and needs a branch-complete reanalysis. read the letter →

arxiv 2411.13316 v1 pith:HAZO4UUH submitted 2024-11-20 gr-qc

Yongbin Du , Yunlong Liu , Xiangdong Zhang This is my paper · ORCID
classification gr-qc MSC 83C5783C1083C45 PACS 04.70.Bw04.60.Pp
keywords spinningparticlesinnermoststablecircularorbitloopquantumgravitycovariantblackholemetricseffectivepotentialpole-dipoleapproximationSchwarzschilddeviationgravitationalwaves
topics Quantum Gravity
open problems Quantum Gravity
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

Loop quantum gravity modifies the Schwarzschild geometry in two covariance-preserving ways, both controlled by a quantum parameter $\zeta$. This paper asks whether those modifications change the last stable circular orbit, the ISCO, of a spinning test particle. Using the pole-dipole equations of motion, it finds that in the first effective metric the ISCO disappears once $\zeta$ exceeds about 4.55, and a particle with orbital angular momentum $l\approx 0.0329$ can hover at a fixed radius above the black hole; in the second metric the ISCO survives even at large $\zeta$, but the allowed spin range shrinks. The payoff is a concrete, near-horizon signature of quantum geometry that could be probed in orbital and gravitational-wave observations.

What carries the argument

The machinery is the pole-dipole equations of motion for a spinning test body (the MPD system), which couple the particle's spin to spacetime curvature and make its 4-velocity deviate from its 4-momentum, together with a timelike constraint that discards superluminal orbits. From the radial momentum equation the authors build an effective potential $V_{\mathrm{eff}\pm}$; circular orbits are extrema ($V=E$, $\mathrm{d}V/\mathrm{d}r=0$) and the ISCO is the point where the stable and unstable extrema merge ($\mathrm{d}^2V/\mathrm{d}r^2=0$). Inserting the two metric functions $f,h$ from Eqs. (2.2)-(2.5) into this construction is what turns the quantum parameter $\zeta$ into a qualitative change in ISCO structure.

What would settle it

For the first metric with $s=1$ and $\zeta=4.6$, solve the full MPD equations (2.6)-(2.7) numerically without the effective-potential reduction: if the stable and unstable circular-orbit branches still meet at some $l$, the ISCO-disappearance claim is wrong. Separately, check that the purported hovering solution at $l\approx 0.0329$ has $v^r=v^\phi=0$ and $v^a v_a<0$, and compare the ISCO radius predicted at astrophysical $\zeta$ with gravitational-wave inspiral data.

Watch

Extended reading notes

Core claim

The central claim is that the two covariant LQG metrics are not interchangeable for spinning-particle dynamics. For solution 1, the effective potential rises and sharpens as $\zeta$ grows; at spin $s=1$ and $\zeta\approx 4.55$ or larger the stable and unstable branches of circular orbits no longer intersect, so no ISCO exists, and instead a particle can hover above the black hole at $l\approx 0.0329$, a loop-quantum-gravity effect the authors attribute to an effective repulsion. For solution 2, the effective potential flattens as $\zeta$ grows and ISCOs persist for $\zeta$ as large as 20, but the timelike condition makes the allowed spin range narrower, opposite to solution 1. The paper therefore establishes that the quantum parameter can qualitatively change the ISCO structure, depending on which covariance-preserving metric describes the spacetime.

Load-bearing premise

The entire calculation rests on the premise that Eqs. (2.2)-(2.5) are the true semiclassical LQG metrics and that $\zeta$ can be as large as the scanned values; if that premise gives way, the ISCO disappearance and hovering do not describe real black holes.

Editorial extensions

If this is right

  • In the first metric, an ISCO-less black hole would have no sharp transition from inspiral to plunge, and a particle with the right angular momentum could hover, so gravitational-wave or accretion signatures would differ from the Schwarzschild prediction.
  • In the second metric, the ISCO persists but the spin range for stable circular orbits shrinks as $\zeta$ grows, which restricts which spinning compact objects can occupy near-horizon orbits.
  • For both metrics, the ISCO radius, energy, and angular momentum shift with $\zeta$ and with spin sign, giving a quantitative target for distinguishing LQG-corrected orbits from classical ones.
  • The spin-curvature coupling itself grows near the horizon, so the quantum modifications are largest exactly where ISCO measurements are most sensitive.

Reading between the lines

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

  • A test the authors do not perform: because the two metrics behave oppositely under $\zeta$, a precise measurement of ISCO location or of the allowed spin range for an accreting black hole could select between the two covariance-preserving Hamiltonians.
  • If the hovering solution is physical, it implies an effective spin-dependent repulsion near the horizon, so future high-resolution observations of near-horizon emission might look for quasi-static luminous spots rather than orbiting hot spots.
  • The same effective-potential method could be applied to rotating LQG black holes, where spin-curvature effects are stronger; the relevant $\zeta$ for a disappearance may be more accessible in that setting.
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

4 major / 4 minor

Summary. The paper studies the Mathisson-Papapetrou-Dixon dynamics of a spinning test particle in two static, spherically symmetric effective metrics derived from covariant loop quantum gravity. Both metrics reduce to Schwarzschild as the quantum parameter ζ→0. The authors derive the radial momentum and the two effective-potential branches V_eff±, impose the standard ISCO conditions together with the timelike constraint, and scan the (ζ, s, l) parameter space. The main reported findings are that, for the first metric, at s=1 and ζ≳4.55, the V_eff+ circular-orbit branches no longer merge so that no ISCO exists and particles can hover, whereas for the second metric ISCOs persist but with a shrinking allowed spin range.

Significance. If fully established, the first result would be a striking qualitative effect: loop-quantum-gravity corrections would eliminate the ISCO for spinning particles and permit hovering configurations. The paper uses a standard and appropriate formalism, and the ζ→0 limit correctly reproduces known Schwarzschild behavior. The comparison between the two covariant metrics is interesting and the numerical exploration is systematic. However, the headline claim is not yet established because the ISCO analysis is restricted to the V_eff+ branch while the paper itself identifies timelike circular orbits on V_eff−; moreover, no code or data are provided to make the numerical threshold reproducible.

major comments (4)
  1. [Sec. III.A, III.B, and Fig. 4(d); Eqs. (3.6)-(3.7)] The ISCO-disappearance claim for solution 1 is established only on the V_eff+ branch. The paper explicitly states in Sec. III.A that V_eff− can attain positive values, and Fig. 4(d) shows a small but present timelike-circular-orbit region for V_eff− at ζ=1. No analysis of V_eff− is given for ζ>4.55. Therefore the Sec. V conclusion that "the entire spacetime no longer possesses an ISCO" is not supported by the presented evidence. Please compute the ISCO conditions (3.8)-(3.10) for V_eff− at large ζ, or restrict the claim to the V_eff+ branch.
  2. [Abstract and Sec. III.B, Fig. 3(a)] The claim that the ISCO disappears for ζ greater than about 4.55 is presented in the abstract as a property of the first metric, but the calculation is performed only for s=1; Fig. 3(a) is explicitly labeled s=1. The abstract needs the s=1 qualifier. In addition, the body uses both 4.55 and 4.56 as the critical value, so the threshold should be pinned down with a reproducible numerical computation before it is quoted in the abstract.
  3. [Sec. III.B, Fig. 5(c),(f)] The hovering solution is presented as a consequence of ISCO disappearance, but only one parameter set (s=1, l≈0.0329, ζ=4.6) is shown. The text does not give the hovering radius, does not state whether the timelike condition (2.32) is satisfied at that radius, and does not explain whether the solution is stable. Please provide the full parameter set, the value of v^μ v_μ, and a stability check, and clarify how this solution relates to both V_eff+ and V_eff−.
  4. [Sec. II.A, Eq. (2.5), and Sec. V] The displayed definition of the quantum parameter ζ is dimensionally unclear, and the admissible range of ζ is never discussed. If ζ is tied to the Planck length and black-hole mass as written, ζ would be extremely small for astrophysical black holes, which would make the ζ≳4.55 regime inaccessible. Please clarify the normalization of ζ and state whether the large-ζ values used in the figures are compatible with the effective Hamiltonian construction of Refs. [68,69].
minor comments (4)
  1. [Sec. II.B and Eq. (3.1)] The notation is inconsistent: Eq. (3.1) uses \hat p^r, while Eq. (2.30) uses p^r, and the dimensionless-variable convention introduced after Eq. (2.31) is not consistently followed in later equations.
  2. [Sec. IV.B, Fig. 8] The text says "As shown in the left panel of Fig. 3" in the discussion of solution 2, but the relevant figure is Fig. 8, not Fig. 3.
  3. [References] References [31] and [36] are duplicates of the same paper, as are references [70] and [73]; please merge the duplicates.
  4. [Tables I and II] The boundary spin values sc and se are quoted to three decimal places, but no numerical method or precision is described; given the 4.55/4.56 discrepancy in the main text, the tables should state how the entries were computed and their numerical uncertainty.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: ISCO results are computed from externally cited LQG metrics via standard MPD equations, with no fitted parameter or self-referential reduction.

full rationale

The paper's derivation chain is self-contained after adopting the two effective metrics (Eq. 2.1 with 2.2-2.3 and 2.4-2.5) from Refs. [68,69], which are external works with no author overlap with the present paper. The subsequent analysis applies the standard Mathisson-Papapetrou-Dixon equations, the Tulczyjew spin condition, conserved quantities, and the effective-potential conditions for circular orbits and ISCO (Eqs. 3.8-3.10). No parameter is fitted to the target ISCO result: the quantum parameter zeta is an input from the cited LQG construction, and the ISCO conditions are imposed on the derived effective potential, not used to define zeta. The Schwarzschild limit (zeta -> 0) is checked against the independent result of Ref. [36]. The self-citations (Refs. [63,64,66]) appear only as background on LQG black holes and do not carry the load-bearing premises of the calculation. The only notable caveat is that the conclusion in Sec. V that 'the entire spacetime no longer possesses an ISCO' is established using the V_eff+ branch, while Fig. 4(d) shows V_eff- also admits timelike circular orbits; this is a completeness/correctness concern about the strength of the claim, not a circularity in the derivation. Accordingly, no circular step is identified.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central calculation is carried out in two metrics imported from the cited LQG literature, using the standard MPD framework and an effective-potential criterion for ISCO. No new free parameters are fitted; ζ and the spin and orbital parameters are scanned inputs. The main epistemic debts are the correctness of the metrics, the validity of the pole-dipole test-particle model, and the identification of ISCO with an inflection of the effective potential.

free parameters (1)
  • ζ (LQG quantum parameter) = scanned 0-20 in figures
    Input from Refs. [68,69], not fitted to data here; the ISCO-disappearance and spin-range results depend on sweeping ζ to values much larger than the Planck-scale estimate would imply.
assumptions (5)
  • domain assumption The two effective metrics (2.2)-(2.5) are the correct covariant LQG black hole solutions of Refs. [68,69].
    All calculations use these metrics as background; if the covariance-preserving effective Hamiltonian used there is not the right one, the results do not describe LQG black holes. Invoked in Section II.A.
  • domain assumption Mathisson-Papapetrou-Dixon equations with the Tulczyjew-Dixon condition S^{ab}p_b=0 govern spinning particle motion.
    Central dynamical framework, Eqs. (2.6)-(2.8); this is standard but is a modeling choice about the test particle.
  • domain assumption The effective potential roots V_eff± from Eqs. (3.6)-(3.7) and conditions (3.8)-(3.10) determine the ISCO.
    Standard method in the cited literature [36,37], but stability of MPD orbits is not rigorously equivalent to an inflection of this effective potential in general.
  • domain assumption The timelike condition (2.32), v^a v_a<0, is the correct physicality filter, and orbits violating it are discarded.
    Used to define allowed parameter regions in Figs. 4 and 9; the pole-dipole approximation can produce superluminal solutions, so this filter is necessary.
  • ad hoc to paper Negative-branch circular orbits near r≈2M in solution 1 are physically meaningful.
    Section III.A and Fig. 1 include V_eff- orbits in a radius range that may include regions between the inner and outer horizons; the paper does not establish these are exterior orbits.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Spinning Particle Dynamics and ISCO in Covariant Loop Quantum Gravity." pith.science (2026). https://pith.science/paper/HAZO4UUH

@misc{pith2026241113316,
  author       = {Pith},
  title        = {Pith review of: Spinning Particle Dynamics and ISCO in Covariant Loop Quantum Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HAZO4UUH}},
  note         = {Machine review of arXiv:2411.13316}
}
abstract

In this paper, we investigate the motion of spinning particles in the background of covariant loop quantum gravity black holes, focusing on two distinct effective metric solutions. Both metrics incorporate a quantum parameter $\zeta$, which quantifies loop quantum corrections. When $\zeta$ approaches zero, the spacetime reduces to the classical Schwarzschild solution. Using the pole-dipole approximation, we derive the equations of motion for spinning particles, accounting for the spin-curvature coupling. Our analysis reveals significant deviations in the behavior of the Innermost Stable Circular Orbit (ISCO) due to quantum effects. In the first effective metric, as $\zeta$ increases, the ISCO's radial position shifts, and for sufficiently large values of $\zeta$ (greater than 4.55), the ISCO disappears, allowing particles to hover above the black hole or oscillate radially. In contrast, in the second metric, ISCOs persist even for large values of $\zeta$, albeit with a more restrictive spin range. These findings highlight the impact of loop quantum gravity corrections on the dynamics of spinning particles and provide insights into potential observational consequences for gravitational wave detections.

Figures

Figures reproduced from arXiv: 2411.13316 by the authors.

Figure 1
Figure 1. FIG. 1. Effective potential curves [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The variation of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The radius of circular orbits as the function of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Allowed region of timelike circular orbits in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Subplot ( [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. ISCO parameter [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The variation of [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. The radius of circular orbits as the function of [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 10
Figure 10. Figure 10: We also provide the numerical results for [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Allowed region for timelike circular orbits in [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. ISCO parameter [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Evaporation and fate of covariant quantum black holes

    gr-qc 2026-07 conditional novelty 5.0 of 10

    For a covariant LQG black-hole metric, Hawking mass-loss rates depend on emitted-particle spin and deviate from Schwarzschild rates only for sub-Planckian masses.

Reference graph

Works this paper leans on

79 extracted references · 64 canonical work pages · cited by 1 Pith paper

  1. [1]

    Moreover, larger values of ζ impose stricter constraints on the allowable spin range for the ISCO, which is in stark contrast to the behavior observed in solution 1. This prompts us to consider that, although both metrics represent quantum corrections to gravity under the aim of preserving covariance, their effects on the behavior of orbiting particles, p...

    work page

  2. [2]

    Spinning test-particles in general relativity. I,

    A. Papapetrou, “Spinning test-particles in general relativity. I,” Proc. R. Soc. A 209, 248–258 (1951)

    work page 1951

  3. [3]

    Observation of Gravitational Waves from a Binary Black Hole Merger,

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “Observation of Gravitational Waves from a Binary Black Hole Merger,” Phys. Rev. Lett.116, 061102 (2016)

    work page 2016

  4. [4]

    GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence,

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence,” Phys. Rev. Lett.116, 241103 (2016)

    work page 2016

  5. [5]

    GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2,

    B. P. Abbott et al.(LIGO Scientific Collaboration and Virgo Collaboration), “GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2,” Phys. Rev. Lett.118, 221101 (2017)

    work page 2017

  6. [6]

    GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence,

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence,” Phys. Rev. Lett.119, 141101 (2017)

    work page 2017

  7. [7]

    GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral,

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral,” Phys. Rev. Lett.119, 161101 (2017)

    work page 2017

  8. [8]

    GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs,

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs,” Phys. Rev. X 9, 031040 (2019)

    work page 2019

Show all 79 references
  1. [9]

    GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo during the First Half of the Third Observing Run,

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo during the First Half of the Third Observing Run,” Phys. Rev. X11, 021053 (2021)

    2021

  2. [10]

    Gravitational waves from inspiraling compact binaries,

    S. Suzuki and K. Maeda, “Gravitational waves from inspiraling compact binaries,” Phys. Rev. D 58, 023005 (1998)

    1998

  3. [11]

    Fully General Relativistic Simulations of Black Hole-Accretion Disk Sys- tems,

    M. Shibata, K. Taniguchi, and T. Nakamura, “Fully General Relativistic Simulations of Black Hole-Accretion Disk Sys- tems,” Prog. Theor. Phys. Suppl. 128, 295 (1997)

    1997

  4. [12]

    Non-rotating Neutron Stars with Quark Matter Cores,

    J. L. Zdunik, P. Haensel, D. Gondek-Rosinska, and E. Gourgoulhon, “Non-rotating Neutron Stars with Quark Matter Cores,” Astron. Astrophys. 372, 535 (2001)

    2001

  5. [13]

    Neutron Star Merger Simulations with Relativistic Codes,

    T. W. Baumgarte, “Neutron Star Merger Simulations with Relativistic Codes,” AIP Conf. Proc. 575, 176 (2001)

    2001

  6. [14]

    Binary neutron star systems: From post-Newtonian approximations to fully relativistic numerical models,

    P. Grandclement, E. Gourgoulhon, and S. Bonazzola, “Binary neutron star systems: From post-Newtonian approximations to fully relativistic numerical models,” Phys. Rev. D 65, 044021 (2002)

    2002

  7. [15]

    Magnetized Neutron Star Mergers in Full General Relativity,

    M. A. Miller, P. Gressman, and W. M. Suen, “Magnetized Neutron Star Mergers in Full General Relativity,” Phys. Rev. D 69, 064026 (2004)

    2004

  8. [16]

    Coupled quark-hadron equations of state in neutron star mergers,

    P. Marronetti, M. D. Duez, S. L. Shapiro, and T. W. Baumgarte, “Coupled quark-hadron equations of state in neutron star mergers,” Phys. Rev. Lett. 92, 141101 (2004)

    2004

  9. [17]

    Effects of quark matter on the neutron star inspiral,

    D. Gondek-Rosinska, M. Bejger, T. Bulik, E. Gourgoulhon, P. Haensel, F. Limousin, and L. Zdunik, “Effects of quark matter on the neutron star inspiral,” Adv. Space Res. 39, 271 (2007)

    2007

  10. [18]

    Spin dynamics of black-hole binaries: Precession and merger,

    M. Campanelli, C. O. Lousto, and Y. Zlochower, “Spin dynamics of black-hole binaries: Precession and merger,” Phys. Rev. D 73, 061501 (2006). 13

    2006

  11. [19]

    Models of Rotating Black Holes in Higher Dimensions,

    P. Shahrrear and S. B. Faruque, “Models of Rotating Black Holes in Higher Dimensions,” Int. J. Mod. Phys. D 16, 1863 (2007)

    2007

  12. [20]

    Ultraluminous X-ray Sources as Black Hole Binaries,

    C. Cabanac, R. P. Fender, R. J. H. Dunn, and E. G. Koerding, “Ultraluminous X-ray Sources as Black Hole Binaries,” Mon. Not. R. Astron. Soc. 396, 1415 (2009)

    2009

  13. [21]

    Electromagnetic radiation from relativistic charged particles in magnetized Kerr black hole,

    A. Abdujabbarov and B. Ahmedov, “Electromagnetic radiation from relativistic charged particles in magnetized Kerr black hole,” Phys. Rev. D 81, 044022 (2010)

    2010

  14. [22]

    Detecting gravitational waves from inspiraling neutron stars,

    S. Hadar, B. Kol, E. Berti, and V. Cardoso, “Detecting gravitational waves from inspiraling neutron stars,” Phys. Rev. D 84, 047501 (2011)

    2011

  15. [23]

    Radiation reaction on the ISCO of compact binaries,

    S. Akcay, L. Barack, T. Damour, and N. Sago, “Radiation reaction on the ISCO of compact binaries,” Phys. Rev. D 86, 104041 (2012)

    2012

  16. [24]

    Resonance frequencies of rapidly rotating Kerr black holes,

    S. Hod, “Resonance frequencies of rapidly rotating Kerr black holes,” Phys. Rev. D 87, 024036 (2013)

    2013

  17. [25]

    The ISCO of spinning particles in Kerr spacetime: implications for accretion disk,

    C. Chakraborty, “The ISCO of spinning particles in Kerr spacetime: implications for accretion disk,” Eur. Phys. J. C 74, 2759 (2014)

    2014

  18. [26]

    Quasi-normal modes of charged black holes,

    S. Hod, “Quasi-normal modes of charged black holes,” Eur. Phys. J. C 74, 2840 (2014)

    2014

  19. [27]

    Acceleration of particles near rotating black holes,

    O. B. Zaslavskii, “Acceleration of particles near rotating black holes,” Eur. Phys. J. C 75, 403 (2015)

    2015

  20. [28]

    Motion of spinning particles in the Schwarzschild field: Circular orbits,

    P. I. Jefremov, O. Yu. Tsupko, and G. S. Bisnovatyi-Kogan, “Motion of spinning particles in the Schwarzschild field: Circular orbits,” Phys. Rev. D 91, 124030 (2015)

    2015

  21. [29]

    Neue Mechanik materieller Systeme,

    M. Mathisson, “Neue Mechanik materieller Systeme,” Acta Phys. Pol. 6, 163 (1937)

    1937

  22. [30]

    Spinning particles around a Schwarzschild black hole: Circular orbits,

    G. Lukes-Gerakopoulos, E. Harms, S. Bernuzzi, and A. Nagar, “Spinning particles around a Schwarzschild black hole: Circular orbits,” Phys. Rev. D 96, 064051 (2017)

    2017

  23. [31]

    Gravitational waves from a spinning particle plunging into a Kerr black hole,

    S. Motoyuki, M. Kei-ichi, S. Masaru, and M. Yasushi, “Gravitational waves from a spinning particle plunging into a Kerr black hole,” Phys. Rev. D 58, 064005 (1998)

    1998

  24. [33]

    Mathisson-Papapetrou-Tulczyjew-Dixon equations in ultra-relativistic regime and gravimagnetic moment,

    A. A. Deriglazov and W. G. Ram ´ ırez, “Mathisson-Papapetrou-Tulczyjew-Dixon equations in ultra-relativistic regime and gravimagnetic moment,” Int. J. Mod. Phys. D 26, 1750047 (2016)

    2016

  25. [34]

    Ultrarelativistic spinning particle and a rotating body in external fields,

    A. A. Deriglazov and W. G. Ram ´ ırez, “Ultrarelativistic spinning particle and a rotating body in external fields,” Adv. High Energy Phys. 2016, 376016 (2016)

    2016

  26. [35]

    Relativistic effects due to gravimagnetic moment of a rotating body,

    W. G. Ram ´ ırez and A. A. Deriglazov, “Relativistic effects due to gravimagnetic moment of a rotating body,” Phys. Rev. D 96, 124013 (2017)

    2017

  27. [36]

    Recent progress on the description of relativistic spin: Vector model of spinning particle and rotating body with gravimagnetic moment in general relativity,

    A. A. Deriglazov and W. G. Ram ´ ırez, “Recent progress on the description of relativistic spin: Vector model of spinning particle and rotating body with gravimagnetic moment in general relativity,” Adv. Theor. Math. Phys. 2017, 7397159 (2017)

    2017

  28. [37]

    Innermost stable circular orbit of spinning particle in charged spinning black hole background,

    Y. P. Zhang, S. W. Wei, W. D. Guo, T. T. Sui, and Y. X. Liu, “Innermost stable circular orbit of spinning particle in charged spinning black hole background,” Phys. Rev. D 97, 084056 (2018)

    2018

  29. [38]

    Motion of spinning particles around a polymer black hole in loop quantum gravity,

    K. Chen and S. W. Wei, “Motion of spinning particles around a polymer black hole in loop quantum gravity,” Phys. Rev. D 110, 024041 (2024)

    2024

  30. [39]

    Innermost stable circular orbits of spinning test particles in Schwarzschild and Kerr space-times,

    P. I. Jefremov, O. Yu. Tsupko, and G. S. Bisnovatyi-Kogan, “Innermost stable circular orbits of spinning test particles in Schwarzschild and Kerr space-times,” Phys. Rev. D 91, 124030 (2015)

    2015

  31. [40]

    Spinning test-particles in general relativity. II.,

    E. Corinaldesi and A. Papapetrou, “Spinning test-particles in general relativity. II.,” Proc. R. Soc. A 209, 259 (1951)

    1951

  32. [41]

    Dynamics of extended bodies in general relativity. I. Momentum and angular momentum,

    W. G. Dixon, “Dynamics of extended bodies in general relativity. I. Momentum and angular momentum,” Proc. R. Soc. A 314, 499 (1970)

    1970

  33. [42]

    Ph.D. thesis,

    S. A. Hojman, “Ph.D. thesis,” Princeton University, 1975

    1975

  34. [43]

    Spinning charged test particles in a Kerr-Newman background,

    R. Hojman and S. A. Hojman, “Spinning charged test particles in a Kerr-Newman background,” Phys. Rev. D 15, 2724 (1977)

    1977

  35. [44]

    Can gravitation accelerate neutrinos?,

    S. A. Hojman and F. A. Asenjo, “Can gravitation accelerate neutrinos?,” Classical Quantum Gravity 30, 025008 (2013)

    2013

  36. [45]

    Spinning massive test particles in cosmological and general static spherically symmetric spacetimes,

    N. Zalaquett, S. A. Hojman, and F. A. Asenjo, “Spinning massive test particles in cosmological and general static spherically symmetric spacetimes,” Classical Quantum Gravity 31, 085011 (2014)

    2014

  37. [46]

    Spinning particles in Schwarzschild spacetime: Revisiting the Mathisson- Papapetrou-Dixon equations,

    R. Uchupol, J. V. Sarah, and A. H. Scott, “Spinning particles in Schwarzschild spacetime: Revisiting the Mathisson- Papapetrou-Dixon equations,” Phys. Rev. D 94, 044008 (2016)

    2016

  38. [47]

    Breakdown of Predictability in Gravitational Collapse,

    S. W. Hawking, “Breakdown of Predictability in Gravitational Collapse,” Phys. Rev. D 14, 2460 (1976)

    1976

  39. [48]

    Information in Black Hole Radiation,

    D. N. Page, “Information in Black Hole Radiation,” Phys. Rev. Lett. 71, 3743 (1993)

    1993

  40. [49]

    Average entropy of a subsystem,

    D. N. Page, “Average entropy of a subsystem,” Phys. Rev. Lett. 71, 1291 (1993)

    1993

  41. [50]

    The Information paradox: A Pedagogical introduction,

    S. D. Mathur, “The Information paradox: A Pedagogical introduction,” Class. Quant. Grav. 26, 224001 (2009)

    2009

  42. [51]

    Black Holes: Complementarity or Firewalls?,

    A. Almheiri, D. Marolf, J. Polchinski and J. Sully, “Black Holes: Complementarity or Firewalls?,” JHEP 02, 062 (2013). “Quantum black holes and complementarity,” JHEP 07, 150 (2014). “Firewalls and the black hole information paradox,” JHEP 11, 107 (2012)

    2013

  43. [52]

    New variables for classical and quantum gravity,

    A. Ashtekar, “New variables for classical and quantum gravity,” Phys. Rev. Lett. 57, 2244 (1986)

    1986

  44. [53]

    Loop Space Representation of Quantum General Relativity,

    C. Rovelli and L. Smolin, “Loop Space Representation of Quantum General Relativity,” Nucl. Phys. B 331, 80 (1990)

    1990

  45. [54]

    Weaving a classical geometry with quantum threads,

    A. Ashtekar, C. Rovelli, and L. Smolin, “Weaving a classical geometry with quantum threads,” Phys. Rev. Lett. 69, 237 (1992)

    1992

  46. [55]

    Discreteness of area and volume in quantum gravity,

    C. Rovelli and L. Smolin, “Discreteness of area and volume in quantum gravity,” Nucl. Phys. B 442, 593 (1995)

    1995

  47. [56]

    Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity,

    T. Thiemann, “Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity,” Phys. Lett. B 380, 257 (1996). 14

    1996

  48. [57]

    Spin networks and quantum gravity,

    C. Rovelli and L. Smolin, “Spin networks and quantum gravity,” Phys. Rev. D 52, 5743 (1995)

    1995

  49. [58]

    Quantum theory of geometry I: Area operators,

    A. Ashtekar and J. Lewandowski, “Quantum theory of geometry I: Area operators,” Class. Quant. Grav. 14, A55-A82 (1997)

    1997

  50. [59]

    Quantum spin dynamics (QSD),

    T. Thiemann, “Quantum spin dynamics (QSD),” Class. Quant. Grav. 15, 839 (1998)

    1998

  51. [60]

    Effective Kerr geometry from loop quantum gravity,

    F. Fazzini, “Effective Kerr geometry from loop quantum gravity,” [arXiv:2409.17099 [gr-qc]]

    arXiv

  52. [61]

    Loop Quantum Gravity motivated multihorizon rotating black holes,

    J. Kumar, S. U. Islam, and S. G. Ghosh, “Loop Quantum Gravity motivated multihorizon rotating black holes,” [arXiv:2209.13562 [gr-qc]]

    arXiv

  53. [62]

    Spinning Loop Black Holes,

    F. Caravelli and L. Modesto, “Spinning Loop Black Holes,” Class. Quant. Grav. 27, 245022 (2010), [arXiv:1006.0232 [gr-qc]]

    2010 arXiv

  54. [63]

    Phenomenological Loop Quantum Geometry of the Schwarzschild Black Hole,

    L. Modesto, “Phenomenological Loop Quantum Geometry of the Schwarzschild Black Hole,” Int. J. Theor. Phys. 49, 1649-1683 (2010), [arXiv:0807.0665 [gr-qc]]

    2010 arXiv

  55. [64]

    Solar system constraints of a polymer black hole in loop quantum gravity,

    Y. Liu, Z. Feng, and X. Zhang, “Solar system constraints of a polymer black hole in loop quantum gravity,” Phys. Rev. D 105, 084068 (2022)

    2022

  56. [65]

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

    J. Lin and X. Zhang, “Effective four-dimensional loop quantum black hole with a cosmological constant,” Phys. Rev. D 110, 026002 (2024)

    2024

  57. [66]

    Higher-dimensional quantum Oppenheimer-Snyder model,

    Z. Shi, Y. Ma and X. Zhang, “Higher-dimensional quantum Oppenheimer-Snyder model,” [arXiv:2408.15821 [gr-qc]]

    arXiv

  58. [67]

    Loop Quantum Black Hole,

    X. Zhang, “Loop Quantum Black Hole,” Universe 9, no.7, 313 (2023)

    2023

  59. [68]

    Bojowald, S

    M. Bojowald, S. Brahma, Juan D. Reyes, Covariance in models of loop quantum gravity: Spherical symmetry, Phys. Rev. D 92, 045043 (2015)

    2015

  60. [69]

    Black Holes and Covariance in Effective Quantum Gravity,

    C. Zhang, J. Lewandowski, Y. Ma and J. Yang, “Black Holes and Covariance in Effective Quantum Gravity,” [arXiv:2407.10168 [gr-qc]]

  61. [70]

    Husin Belfaqih, M

    I. Husin Belfaqih, M. Bojowald, S. Brahma, E. I. Duque, Black holes in effective loop quantum gravity: Covariant holonomy modifications, arXiv:2407.12087

    arXiv

  62. [72]

    Investigating the effective potential of the Mathisson-Papapetrou-Dixon equations for a spinning particle in a Kerr spacetime,

    G. Lukes-Gerakopoulos, J. Seyrich, and D. Kunst, “Investigating the effective potential of the Mathisson-Papapetrou-Dixon equations for a spinning particle in a Kerr spacetime,” Phys. Rev. D 90, 104019 (2014)

    2014

  63. [73]

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

    J. Ben Achour, S. Brahma, and A. Marciano, “Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections,” Phys. Rev. D 96, 026002 (2017), [arXiv:1608.07314 [gr- qc]]

    2017 arXiv

  64. [74]

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

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

    2024

  65. [75]

    S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time,Cambridge Monographs on Mathematical Physics (Cambridge University Press, 1973)

    1973

  66. [76]

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

    J. M¨ unch, “Causal structure of a recent loop quantum gravity black hole collapse model,” Phys. Rev. D 104, 046019 (2021), [arXiv:2103.17112 [gr-qc]]

    2021 arXiv

  67. [77]

    Quantum Oppenheimer-Snyder and Swiss Cheese Models,

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

    2023 arXiv

  68. [78]

    Quantum extension of the Kruskal spacetime,

    A. Ashtekar, J. Olmedo, and P. Singh, “Quantum extension of the Kruskal spacetime,” Phys. Rev. D 98, 126003 (2018), [arXiv:1806.02406 [gr-qc]]

    2018 arXiv

  69. [79]

    Quantum Nature of the Big Bang: An Analytical and Numerical Investigation. I,

    A. Ashtekar, T. Pawlowski, and P. Singh, “Quantum Nature of the Big Bang: An Analytical and Numerical Investigation. I,” Phys. Rev. D 73, 124038 (2006), [arXiv:gr-qc/0604013]

    2006 arXiv

  70. [80]

    Quantum Nature of the Big Bang: Improved dynamics,

    A. Ashtekar, T. Pawlowski, and P. Singh, “Quantum Nature of the Big Bang: Improved dynamics,” Phys. Rev. D 74, 084003 (2006), [arXiv:gr-qc/0607039]

    2006 arXiv

  71. [81]

    On Continued gravitational contraction,

    J. R. Oppenheimer and H. Snyder, “On Continued gravitational contraction,” Phys. Rev. 56, 455–459 (1939)

    1939

Pith tools

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