Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Radiative Back-Reaction on Charged Particle Motion in the Dipole Magnetosphere of Neutron Stars

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read Radiative back-reaction in a neutron star's dipole magnetosphere sends charged particles onto the surface when the Lorentz force is attractive, and widens their orbits when it is repulsive.

desk verdict First systematic LL radiation-reaction study in a dipole NS magnetosphere with a genuinely new vertical-widening effect, but the unquantified tail term is the same order as the local terms in the simulated regime, so the classification is conditional. read the letter →

arxiv 2412.04996 v1 pith:OB2SMO5F submitted 2024-12-06 astro-ph.HE gr-qc

Zdeněk Stuchlík , Jaroslav Vrba , Martin Kološ , Arman Tursunov This is my paper · ORCID
classification astro-ph.HEgr-qc
keywords radiationreactionLandau-Lifshitzequationneutronstarmagnetospheredipolemagneticfieldchargedparticledynamicsoff-equatorialcircularorbitsorbitalwideningeffectivepotential
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 asks what the radiation reaction does to a charged particle orbiting a magnetized neutron star, treating the star as a static, spherically symmetric spacetime with a dipole magnetic field and a surface at $R=3M$. The answer it defends is that the sign of the Lorentz force decides everything. When the force is attractive (magnetic parameter $b>0$ for corotating particles), the back-reaction always drains energy and angular momentum, and every studied bound, epicyclic, or chaotic orbit ends on the stellar surface. When the force is repulsive ($b<0$), the back-reaction instead drives stable equatorial circular orbits outward, and off-equatorial orbits either migrate toward the equator and then widen, or fall onto the star, with a numerically determined critical latitude separating the two fates. This matters because it controls whether radiating charge around neutron stars accumulates in expanding belts or precipitates onto the surface, with observable consequences for quasi-periodic oscillations, radiation belts, and polar aurora-like impacts.

What carries the argument

The machinery is the combination of the conservative effective potential $V_{\mathrm{eff}}(r,\theta;L,b)$, whose local extrema give the equatorial and off-equatorial circular orbits and whose Hessian governs their stability, with the Landau-Lifshitz form of the radiation-reaction equation, obtained from the DeWitt-Brehme equation by dropping the Ricci and non-local tail terms. The magnetic parameter $b = qB/m$ encodes the strength of the Lorentz force relative to gravity, and the reaction parameter $k = 2q^2/(3mGM)$ sets the radiation-reaction strength. The load-bearing identity is the local term $\frac{q k}{m} F^\alpha{}_{\beta;\alpha}u^\beta u^\mu$, which the paper's numerical experiments single out as the source of orbital widening and of the accompanying increase in specific energy and angular momentum. The critical latitude $\theta_{w/f}(b)$ is defined by the off-equatorial orbit that separates the widening basin from the fall basin.

What would settle it

Integrate the full DeWitt-Brehme equation, retaining the tail integral (52), for a representative repulsive case such as $b = -2$ with radiation-reaction parameter $k = 0.1$, starting from a stable off-equatorial orbit. If the orbit still drifts outward and gains specific energy, the local-term explanation survives; if it falls onto the surface instead, the neglected tail term controls the outcome and the reported classification is an artifact of the local approximation.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that the Landau-Lifshitz approximation to the DeWitt-Brehme equation, applied to charged test particles in a dipole magnetosphere, produces two qualitatively different long-term behaviors. For an attractive Lorentz force ($b>0$) the back-reaction acts as pure damping: equatorial circular orbits, epicyclic motion, and chaotic belts all end with the particle falling onto the neutron star surface. For a repulsive Lorentz force ($b<0$) the back-reaction can do work: stable equatorial circular orbits undergo orbital widening, with both specific energy and specific angular momentum increasing over time, and off-equatorial circular orbits slide along the family of off-equatorial orbits either toward the equator, where they widen with growing vertical oscillations, or toward the surface, depending on whether the initial latitude lies above or below a critical value $\theta_{w/f}(b)$. The paper reports vertical orbital widening as a new effect not seen in a uniform magnetic field, attributes it to the inhomogeneity of the dipole field, and identifies the Maxwell-tensor derivative term in the Landau-Lifshitz equation as the one responsible for the energy gain.

Load-bearing premise

The calculations assume that the delayed, non-local part of the radiation reaction, radiation that curves through the spacetime and returns to the particle, never matters because the neutron star's surface at $R=3M$ absorbs any returning radiation before it acts; all reported widening and energy gain are carried by the local part of the reaction, and a significant delayed contribution could reverse them.

Editorial extensions

If this is right

  • Under an attractive Lorentz force, radiating charge cannot remain on any bound orbit: every tested equatorial, off-equatorial, epicyclic, or chaotic trajectory ends on the surface, so radiative losses hasten accretion onto the star.
  • Under a repulsive Lorentz force, stable equatorial orbits expand, so a radiating particle can move outward while emitting synchrotron radiation, transporting angular momentum away from the star in the process.
  • Off-equatorial particles starting above the critical latitude $\theta_{w/f}(b)$ first slide to the equator and then widen; below it they precipitate onto the star, giving a latitude-selected fate for radiation belts.
  • The critical latitude $\theta_{w/f}(b)$ is independent of the radiation-reaction parameter $k$, so the widening-versus-fall classification does not depend on the reaction strength even though the timescales do.
  • Vertical oscillation amplitude grows during widening, a signature specific to the dipole field and absent in uniform-field models, so the dipole geometry itself shapes the late-time motion.

Reading between the lines

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

  • If the local-term energy gain is real and is not cancelled by the tail term, a radiating charged particle in a dipole field acts as a small energy-extraction engine, gaining specific energy from the field structure while emitting radiation; an astrophysical test would be to search for gradual outward migration of X-ray-emitting hot spots or rings around magnetized neutron stars.
  • The same Landau-Lifshitz machinery with the tail term included is known to behave differently around black holes, so applying the full DeWitt-Brehme equation to a black hole in a dipole field would determine whether the widening-versus-fall dichotomy persists or is replaced by tail-driven behavior.
  • Real neutron stars rotate, which adds an electric field and a unipolar-inductor potential that the static model omits; rotation could shift the critical latitude and turn the predicted polar fall into a voltage-driven outflow.
  • Because the critical latitude is independent of the reaction strength $k$, the same classification should apply to dust, protons, and electrons once rescaled, so the effect could be searched for across very different particle populations around the same star.
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. This paper studies the motion of charged test particles in the exterior of a non-rotating neutron star modeled by the Schwarzschild metric with a dipole magnetic field. It first characterizes conservative equatorial and off-equatorial circular orbits and their associated belts using an effective potential. It then integrates the Landau-Lifshitz equation with the DeWitt-Brehme tail term neglected, for large (illustrative) radiation-reaction parameters k=0.1 and 0.01, and classifies the outcomes: under an attractive Lorentz force the radiation reaction drives particles to the stellar surface, while under a repulsive Lorentz force stable circular orbits widen and off-equatorial orbits either migrate to the equator and widen or fall to the surface, with a numerically determined critical latitude θ_w/f(b).

Significance. The paper provides a systematic numerical catalog of radiation-reaction effects in a dipole magnetosphere, extending the authors' earlier work on conservative motion. The analytic effective-potential analysis of off-equatorial orbits is useful, and the comparison between orbits with and without radiation reaction is clearly presented. If the classification survives a quantitative treatment of the tail term, the predicted widening/fall boundary and the vertical widening of oscillatory orbits would be interesting, falsifiable features for models of charged dust or plasmoids in neutron-star magnetospheres. The manuscript is honest about the illustrative character of the large k values and about the open tail-term problem; however, the central claims currently rest on an unquantified truncation and on an unshown term-by-term attribution, which is why I recommend major revision.

major comments (3)
  1. [Section V, Eq. (53)] The neglect of the tail term in Eq. (52) is load-bearing but unquantified. The argument that the Schwarzschild reflective barrier is hidden beneath the NS surface at R=3M and that radiation entering the surface is captured does not exclude curvature-scattering contributions to the tail from the exterior region r>3M; for synchrotron-type orbits part of the scattered field can return on orbital timescales before reaching the surface. Refs. [70,71] show for magnetized Schwarzschild backgrounds that the tail can be comparable to or dominate the local terms and can change the sign of the energy transfer. Since Fig. 19 and the widening/fall classification are the paper's central quantitative output, I request a quantitative estimate of the relative size of the tail term for representative parameters (e.g., the cases of Fig. 18), or a computation including the tail via the methods of Refs. [70,71] for a subset of trajectories, before the classification can be considered robust.
  2. [Section VI.B.4, Fig. 25] The attribution of the energy increase during orbital widening to the q k/m F^α_{β;α} u^β u^μ term rests on the statement that 'preliminary calculations confirm' this, but the supporting calculation is not shown. This is load-bearing because Section VI.B.4 uses the energy increase to explain the counter-intuitive widening effect, and because the same term may be sensitive to the neglected tail. Please show the decomposition of dE/dτ and dL/dτ into the Lorentz, FRR1, and FRR2 contributions for at least one widening and one falling trajectory, or otherwise provide the calculation that isolates the Maxwell-derivative term.
  3. [Section VI.B.2, Fig. 19] The critical latitude θ_w/f(b) is presented as independent of the RR parameter k, and Fig. 19 is labeled 'For all k', but the numerical evidence shown is only for k=0.1 and k=0.01 (and for a few values of b). If the independence is a genuine property of the LL dynamics, it requires either an analytic argument or a convergence study over a wider range of k (including values closer to realistic k~10^{-18} for electrons or dust, where the widening timescale may change qualitatively). As it stands, the claim that Fig. 19 applies 'for all k' exceeds the presented evidence.
minor comments (5)
  1. [Section VI.B.2] The verbal specification of the three regimes contains reversed inequalities: 'First regime (0 < b < -0.654)' should read '-0.654 < b < 0', and the second and third regimes are similarly misordered.
  2. [Section IV, Eq. (53)] The last term on the right-hand side of Eq. (53) ends with a bare 'uμ' after an expression that already contains u^μ; the index structure appears to have a typo and should be checked.
  3. [Reference [22]] Reference [22] is cited as 'Submitted .., .. (2024), arXiv:... [astro-ph.HE]' with placeholder text; it should be updated to the published or arXiv identifier before publication.
  4. [Fig. 2] The 'Stable' labels in Fig. 2 do not clearly indicate which side of each curve (brISCO or bθISCO) is stable; please add explicit shading or arrow annotations defining the stability region.
  5. [Section III.C, Eqs. (28)-(30)] The subscript 'Coff' for off-equatorial circular orbits is introduced after the equations that use it; clarify the notation and distinguish it from the subscript 'c' used for equatorial circular orbits.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the RR trajectories and the widening/fall boundary are read directly from numerical integrations of Eq. (53), not fitted to the conclusions; self-citations supply context but the needed formulas are reproduced in this paper.

full rationale

The paper's central derivation chain is self-contained for its principal claims. The conservative part (Sections II and III) starts from the Hamiltonian (10) and the dipole vector potential (3), constructs the effective potential (16), and obtains circular orbits from the simultaneous vanishing of its derivatives; the stability functions brISCO (26) and bthetaISCO (27) are given explicitly or as root conditions, so the companion paper [22] is a context citation rather than a load-bearing black box. The radiation-reaction part (Sections IV and VI) numerically integrates the Landau-Lifshitz equation (53) with stated parameters (b, L, E, k), and the reported fall/widening taxonomy, including the critical latitude theta_w/f(b), is a classification of those same integrations rather than a quantity fitted to an external dataset or to the conclusions; no presented step defines its output in terms of the effect it is meant to predict. The main caveats are limitations and correctness risks, not circularity: the neglect of the tail integral (52) in Eq. (53) is justified in Section V by the surface-capture argument and footnote [73] but is not quantified for backscattering in the exterior region r>3M, and Refs. [70,71] show that tail effects can be important around black holes; Table I's order-of-magnitude estimate Ftail~k is not a bound on the non-local integral (52), so the neglect remains an assumption. Likewise, the attribution of the widening to the local Maxwell-derivative term is supported only by 'preliminary calculations' mentioned in Section VI.B.4. These concerns could shift or erase the reported boundary, but they do not make the derivation tautological. The nonzero score reflects the minor self-citation to the companion analysis [22] and the unquantified tail assumption; no circular reduction was found.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claims rest on a fixed background model (Schwarzschild plus test dipole field), the test-particle approximation, and the Landau-Lifshitz equation with the tail term dropped. The only hand-chosen numbers are the parameters used to generate illustrative trajectories: the magnetic parameter b, the radiation reaction parameter k, and initial conditions. No new entities are introduced.

free parameters (3)
  • RR parameter k = 0.1 and 0.01
    Chosen by hand to make radiation-reaction effects visible; realistic values for electrons around NSs are ~10^-18 (Section IV).
  • magnetic parameter b = values from -1000 to 105 in figures
    Chosen to represent attractive, chaotic, and magnetic regimes; not fitted to data.
  • initial conditions (E, L, r0, theta0) = given per trajectory in figure captions
    Selected to illustrate different classes of motion (circular, epicyclic, chaotic).
assumptions (6)
  • domain assumption Schwarzschild exterior geometry is a valid model for the non-rotating NS spacetime
    Used in Eq. (1); ignores stellar rotation and oblateness.
  • domain assumption The dipole magnetic field of Wasserman-Shapiro is the correct external field configuration
    Eqs. (3)-(5); standard test-field solution in Schwarzschild, ignores plasma effects and self-consistency.
  • domain assumption Test-particle approximation: the particle's charge and mass do not affect the background
    Implicit in Eq. (9); standard for q/m small.
  • ad hoc to paper Landau-Lifshitz equation with tail term dropped is a valid approximation for radiation reaction
    Eq. (53) and Section V; the tail term is neglected using an argument about the NS surface, but no quantitative justification is provided.
  • standard math Stability of circular orbits is governed by the Hessian of the effective potential
    Eq. (19) and (31); standard result for extrema of a 2D potential.
  • domain assumption Identification of motion regimes: |b|<<1 gravitational, |b|~1 chaotic, |b|>>1 magnetic
    Section III.D; based on cyclotron/Kepler frequency comparison.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Radiative Back-Reaction on Charged Particle Motion in the Dipole Magnetosphere of Neutron Stars." pith.science (2026). https://pith.science/paper/OB2SMO5F

@misc{pith2026241204996,
  author       = {Pith},
  title        = {Pith review of: Radiative Back-Reaction on Charged Particle Motion in the Dipole Magnetosphere of Neutron Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OB2SMO5F}},
  note         = {Machine review of arXiv:2412.04996}
}
read the original abstract

The motion of charged particles under the Lorentz force in the magnetosphere of neutron stars, represented by a dipole field in the Schwarzschild spacetime, can be determined by an effective potential, whose local extrema govern circular orbits both in and off the equatorial plane, which coincides with the symmetry plane of the dipole field. In this work, we provide a detailed description of the properties of these "conservative" circular orbits and, using the approximation represented by the Landau-Lifshitz equation, examine the role of the radiative back-reaction force that influences the motion of charged particles following both the in and off equatorial circular orbits, as well as the chaotic orbits confined to belts centered around the circular orbits. To provide clear insight into these dynamics, we compare particle motion with and without the back-reaction force. We demonstrate that, in the case of an attractive Lorentz force, the back-reaction leads to the charged particles falling onto the neutron star's surface in all scenarios considered. For the repulsive Lorentz force, in combination with the back-reaction force, we observe a widening of stable equatorial circular orbits; the off-equatorial orbits shift toward the equatorial plane and subsequently widen if they are sufficiently close to the plane. Otherwise, the off-equatorial orbits evolve toward the neutron star surface. The critical latitude, which separates orbital widening from falling onto the surface, is determined numerically as a function of the electromagnetic interaction's intensity.

Figures

Figures reproduced from arXiv: 2412.04996 by the authors.

Figure 1
Figure 1. FIG. 1: The equipotential surfaces of the 4-vector [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Characteristic stability functions [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Radial profiles of the specific energy and the specific angular momentum at the equatorial circular orbits. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (27 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Specific angular momentum (left panel), specific energy (middle panel) and radial position (right panel) of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Position of the off-equatorial circular orbits for various series of the magnetic parameter [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Radial profiles of specific energy and specific angular momentum of the off-equatorial circular orbits. Notice [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: The latitude coordinate [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: The difference of specific energies of the unstable equatorial and stable off-equatorial circular orbits for the [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Different types of bound closed orbits represent [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Radial [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: Equatorial circular orbits under attractive Lorentz force influence. The motion starts from a stable circular [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: RR influence on the particles moving under attractive Lorentz force in effective potential barrier open in [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13: The RR influence for the motion under attractive Lorentz force with effective potential barrier open in the [PITH_FULL_IMAGE:figures/full_fig_p019_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14: The RR influence for the motion under attractive Lorentz force with effective potential barrier closed in [PITH_FULL_IMAGE:figures/full_fig_p019_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15: The RR influence on the particle following an unstable equatorial circular orbit with [PITH_FULL_IMAGE:figures/full_fig_p020_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16: The RR influence on the particle following a stable equatorial circular orbit with [PITH_FULL_IMAGE:figures/full_fig_p021_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17: The RR influence on the particle oscillating around a stable equatorial circular orbit with [PITH_FULL_IMAGE:figures/full_fig_p022_17.png]
Figure 18
Figure 18. Figure 18: FIG. 18: Widening vs. fall from off-equatorial circular orbits. Depending on the initial latitudinal angle [PITH_FULL_IMAGE:figures/full_fig_p022_18.png]
Figure 19
Figure 19. Figure 19: FIG. 19: Critical latitudinal angle [PITH_FULL_IMAGE:figures/full_fig_p023_19.png]
Figure 20
Figure 20. Figure 20: FIG. 20: Widening of the oscillatory motion around an off-equatorial circular orbit at [PITH_FULL_IMAGE:figures/full_fig_p024_20.png]
Figure 21
Figure 21. Figure 21: FIG. 21: Descend and fall onto the NS surface of the oscillatory motion around an off-equatorial circular orbit at [PITH_FULL_IMAGE:figures/full_fig_p025_21.png]
Figure 22
Figure 22. Figure 22: FIG. 22: The orbital widening related to the chaotic motion under repulsive Lorentz force allowing for existence of [PITH_FULL_IMAGE:figures/full_fig_p026_22.png]
Figure 23
Figure 23. Figure 23: FIG. 23: The fall regime of the chaotic motion under the repulsive Lorentz force and additional RR force for the [PITH_FULL_IMAGE:figures/full_fig_p027_23.png]
Figure 24
Figure 24. Figure 24: FIG. 24: Orbital widening of the chaotic motion under the repulsive Lorentz force giving the equatorial barrier [PITH_FULL_IMAGE:figures/full_fig_p028_24.png]
Figure 25
Figure 25. Figure 25: FIG. 25: Demonstration of the effect of RR force on charged particles moving in a dipole field. The main panel on [PITH_FULL_IMAGE:figures/full_fig_p029_25.png]
Figure 26
Figure 26. Figure 26: FIG. 26: Trajectories representing magnetic regime under magnetic repulsion near the NS surface, constructed for [PITH_FULL_IMAGE:figures/full_fig_p030_26.png]
Figure 27
Figure 27. Figure 27: FIG. 27: Trajectories representing magnetic regime under magnetic repulsion far away from the NS surface, [PITH_FULL_IMAGE:figures/full_fig_p031_27.png]
Figure 28
Figure 28. Figure 28: FIG. 28: Trajectories representing magnetic regime under magnetic repulsion far away from the NS surface, [PITH_FULL_IMAGE:figures/full_fig_p032_28.png]
Figure 29
Figure 29. Figure 29: FIG. 29: Trajectories representing magnetic regime under magnetic attraction, constructed for high magnitude of [PITH_FULL_IMAGE:figures/full_fig_p034_29.png]
Figure 30
Figure 30. Figure 30: FIG. 30: Trajectories representing magnetic regime under magnetic attraction, constructed for the high magnitude [PITH_FULL_IMAGE:figures/full_fig_p035_30.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. From St{\o}rmer to Schwarzschild: Analytical Dynamics of Charged Particles in a Dipole Magnetosphere

    gr-qc 2026-08 conditional novelty 7.0 of 10

    In a Schwarzschild spacetime with a leading-dipole magnetic field, the inner stable charged-particle orbit first moves inward with magnetic coupling, then outward, with the limiting mode switching from radial to verti...

Reference graph

Works this paper leans on

91 extracted references · 58 canonical work pages · cited by 1 Pith paper

  1. [1]

    The fall occurs along a trajectory confined to the equatorial plane – see FIG

    Equatorial circular orbits The RR force acting on particles following unstable or near-marginal stable equatorial circular orbits under the magnetic attraction, where the effective potential is open in the radial direction, always leads to the particle’s immediate onto the NS surface. The fall occurs along a trajectory confined to the equatorial plane – s...

  2. [2]

    ”Smoothing” of epicyclic near-circular motion Particles slightly displaced from the position of a cir- cular orbit in the equatorial plane experience different outcomes depending on the nature of the effective poten- tial barrier corresponding to motion under the Lorentz force. When the barrier is restricted in the radial direc- tion, but open vertically ...

  3. [3]

    Chaotic bound orbits The chaotic motion of particles off the equatorial plane, within large regions around the equatorial circular orbits, is explored in two cases: (i) when the effective barrier under the Lorentz force is open to the NS surface in the radial direction, and (ii) when there is an island bar- rier allowing for trapped motion under the Loren...

  4. [4]

    Under the combined in- fluence of the Lorentz force and the RR force, the or- bits slowly expand, in contrast to the usual shrinking observed with the attractive Lorentz force

    Equatorial circular orbits: widening In the case of equatorial circular orbits, a phenomenon unique to the presence of the repulsive Lorentz force can be observed – orbital widening. Under the combined in- fluence of the Lorentz force and the RR force, the or- bits slowly expand, in contrast to the usual shrinking observed with the attractive Lorentz forc...

  5. [5]

    13: The RR influence for the motion under attractive Lorentz force with effective potential barrier open in the inward radial direction

    Off-equatorial circular orbits: widening vs fall Particles following off-equatorial circular orbits under the influence of the repulsive Lorentz force can exhibit 19 FIG. 13: The RR influence for the motion under attractive Lorentz force with effective potential barrier open in the inward radial direction. FIG. 14: The RR influence for the motion under at...

  6. [6]

    When chaotic motion crosses the equatorial plane, the RR force gradually converts this motion into an orbital widening of chaotic nature, provided that the correspond- 21 FIG

    Chaotic motion in the belts The large-scale chaotic motion in belts, initially gov- erned solely by the Lorentz force, demonstrates similar effects under the additional influence of the RR force as in the previous cases of motion near circular orbits. When chaotic motion crosses the equatorial plane, the RR force gradually converts this motion into an orb...

  7. [7]

    The time evolution of these characteristics revels the signatures of the RR force’s in- fluence on the motion

    Evolution of the motion parameters due to the RR force To gain a deeper understanding of the role of the RR force in the motion of charged test particles, we need to study the time evolution of the key motion parameters, such as the specific energy and specific angular momen- tum under the combined influence of the gravitational, Lorentz, and RR forces. T...

  8. [8]

    S. B. Popov, High magnetic field neutron stars and magnetars in binary systems, IAU Symposium 363, 61 (2023), arXiv:2201.07507 [astro-ph.HE]

    work page Pith review arXiv 2023

Show all 91 references
  1. [9]

    R. P. Eatough, H. Falcke, R. Karuppusamy, K. J. Lee, D. J. Champion, E. F. Keane, G. Desvignes, D. H. F. M. Schnitzeler, L. G. Spitler, M. Kramer, B. Klein, C. Bassa, G. C. Bower, A. Brunthaler, I. Cognard, A. T. Deller, P. B. Demorest, P. C. C. Freire, A. Kraus, A. G. Lyne, A...

    2013 arXiv

  2. [10]

    R. Gold, J. C. McKinney, M. D. Johnson, and S. S. Doeleman, Probing the Magnetic Field Structure in Sgr A* on Black Hole Horizon Scales with Polarized Radia- tive Transfer Simulations, Astrophys. J. 837, 180 (2017), arXiv:1601.05550 [astro-ph.HE]

    2017 arXiv

  3. [11]

    R. A. Daly, Black Hole Spin and Accretion Disk Mag- netic Field Strength Estimates for More Than 750 Ac- tive Galactic Nuclei and Multiple Galactic Black Holes, Astrophys. J. 886, 37 (2019), arXiv:1905.11319 [astro- ph.HE]

    2019 arXiv

  4. [12]

    M. Y. Piotrovich, A. G. Mikhailov, S. D. Buliga, and T. M. Natsvlishvili, Determination of magnetic field strength on the event horizon of supermassive black holes in active galactic nuclei, Monthly Notices of the RAS 495, 614 (2020), arXiv:2004.07075 [astro-ph.HE]

    2020 arXiv

  5. [13]

    Ruffini and A

    R. Ruffini and A. Treves, On a Magnetized Rotating Sphere, Appl. Phys. Lett. 13, 109 (1973)

    1973

  6. [14]

    Prasanna, General-relativistic analysis of charged- particle motion in electromagnetic fields surrounding black holes, La Rivista del Nuovo Cimento (1978-1999) 3, 1 (1980)

    A. Prasanna, General-relativistic analysis of charged- particle motion in electromagnetic fields surrounding black holes, La Rivista del Nuovo Cimento (1978-1999) 3, 1 (1980)

    1980

  7. [15]

    Ruffini and J

    R. Ruffini and J. R. Wilson, Relativistic magnetohydro- dynamical effects of plasma accreting into a black hole, Phys. Rev. D 12, 2959 (1975)

    1975

  8. [16]

    S. V. Dhurandhar and N. Dadhich, Energy-extraction processes from a Kerr black hole immersed in a mag- netic field. I. Negative-energy states, Phys. Rev. D 29, 2712 (1984)

    1984

  9. [17]

    Parthasarathy, S

    S. Parthasarathy, S. M. Wagh, S. V. Dhurandhar, and N. Dadhich, High Efficiency of the Penrose Process of Energy Extraction from Rotating Black Holes Immersed in Electromagnetic Fields, Astrophys. J. 307, 38 (1986)

    1986

  10. [18]

    R. D. Blandford and R. L. Znajek, Electromagnetic ex- traction of energy from Kerr black holes., Monthly No- tices of the RAS 179, 433 (1977)

    1977

  11. [19]

    Dadhich, A

    N. Dadhich, A. Tursunov, B. Ahmedov, and Z. Stuchl ´ ık, The distinguishing signature of magnetic Penrose pro- cess, Monthly Notices of the RAS 478, L89 (2018), 37 arXiv:1804.09679 [astro-ph.HE]

    2018 arXiv

  12. [20]

    Stuchl ´ ık, M

    Z. Stuchl ´ ık, M. Koloˇ s, J. Kov´ aˇ r, P. Slan´ y, and A. Tur- sunov, Influence of Cosmic Repulsion and Magnetic Fields on Accretion Disks Rotating around Kerr Black Holes, Universe 6, 26 (2020)

    2020

  13. [21]

    Koloˇ s, A

    M. Koloˇ s, A. Tursunov, and Z. Stuchl ´ ık, Radiative Pen- rose process: Energy gain by a single radiating charged particle in the ergosphere of rotating black hole, Phys. Rev. D 103, 024021 (2021), arXiv:2010.09481 [gr-qc]

    2021 arXiv

  14. [22]

    Stuchl ´ ık, M

    Z. Stuchl ´ ık, M. Koloˇ s, and A. Tursunov, Penrose Process: Its Variants and Astrophysical Applications, Universe 7, 416 (2021)

    2021

  15. [23]

    Stuchl ´ ık, A

    Z. Stuchl ´ ık, A. Kotrlov´ a, and G. T¨ or¨ ok, Multi-resonance orbital model of high-frequency quasi-periodic oscilla- tions: possible high-precision determination of black hole and neutron star spin, Astronomy and Astrophysics Jour- nal 552, A10 (2013), arXiv:1305.3552 [ast...

    2013 arXiv

  16. [24]

    Koloˇ s, Z

    M. Koloˇ s, Z. Stuchl ´ ık, and A. Tursunov, Quasi- harmonic oscillatory motion of charged particles around a Schwarzschild black hole immersed in a uniform mag- netic field, Classical and Quantum Gravity 32, 165009 (2015), arXiv:1506.06799 [gr-qc]

    2015 arXiv

  17. [25]

    Koloˇ s, A

    M. Koloˇ s, A. Tursunov, and Z. Stuchl ´ ık, Possible sig- nature of the magnetic fields related to quasi-periodic oscillations observed in microquasars, European Physi- cal Journal C 77, 860 (2017), arXiv:1707.02224 [astro- ph.HE]

    2017 arXiv

  18. [26]

    P´ anis, M

    R. P´ anis, M. Koloˇ s, and Z. Stuchl ´ ık, Determination of chaotic behaviour in time series generated by charged particle motion around magnetized Schwarzschild black holes, European Physical Journal C 79, 479 (2019), arXiv:1905.01186 [gr-qc]

    2019 arXiv

  19. [27]

    Stuchl ´ ık, M

    Z. Stuchl ´ ık, M. Koloˇ s, and A. Tursunov, Large-scale mag- netic fields enabling fitting of the high-frequency QPOs observed around supermassive black holes, Publications of the Astronomical Society of Japan 74, 1220 (2022)

    2022

  20. [28]

    The tidal charge in the braneworld models of NSs [77] can be also well applied for fitting the data of HF QPOs in binary systems containing a NS [78]

  21. [29]

    J. Vrba, M. Koloˇ s, and Z. Stuchl ´ ık, Charged particles in dipole magnetosphere of neutron stars: epicyclic oscilla- tions in and off equatorial plane, Submitted .., .. (2024), arXiv:... [astro-ph.HE]

    2024

  22. [30]

    T¨ or¨ ok, P

    G. T¨ or¨ ok, P. Bakala, E. ˇSr´ amkov´ a, Z. Stuchl ´ ık, and M. Urbanec, On Mass Constraints Implied by the Rel- ativistic Precession Model of Twin-peak Quasi-periodic Oscillations in Circinus X-1, Astrophys. J. 714, 748 (2010), arXiv:1008.0088 [astro-ph.HE]

    2010 arXiv

  23. [31]

    For non- rotating compact objects such an extreme acceleration is not possible [17]

    The Lorentz force acting on electrons or protons (ions) in vicinity of the event horizon of magnetized rotating BHs, or the surface of magnetized rotating NSs can cause their enormous acceleration [13, 15, 79, 80] because of the electric component of the electromagnetic field ...

  24. [32]

    Recall that in the charged Kerr-Newman-(de Sitter) spacetimes the motion of charged test particles is fully regular and can be given in terms of elliptic integrals [31, 55, 81–84]

  25. [33]

    Tursunov, M

    A. Tursunov, M. Koloˇ s, Z. Stuchl ´ ık, and D. V. Gal’tsov, Radiation Reaction of Charged Particles Orbiting a Mag- netized Schwarzschild Black Hole, Astrophys. J. 861, 2 (2018), arXiv:1803.09682 [gr-qc]

    2018 arXiv

  26. [34]

    Stuchl ´ ık, M

    Z. Stuchl ´ ık, M. Koloˇ s, A. Tursunov, and D. Gal’tsov, On the Role of the Tail Term in Electromagnetic Radiation Reaction, Universe 10, 249 (2024)

    2024

  27. [35]

    B. S. DeWitt and R. W. Brehme, Radiation damping in a gravitational field, Annals of Physics 9, 220 (1960)

    1960

  28. [36]

    L. D. Landau and E. M. Lifshitz, Course of theoret- ical physics - Pergamon International Library of Sci- ence, Technology, Engineering and Social Studies, Ox- ford: Pergamon Press, 1975, 4th rev.engl.ed. (Pergamon Press, 1975)

    1975

  29. [37]

    A. A. Tursunov, M. Koloˇ s, and Z. Stuchl ´ ık, Orbital widening due to radiation reaction around a magnetized black hole, Astronomische Nachrichten 339, 341 (2018), arXiv:1806.06754 [gr-qc]

    2018 arXiv

  30. [38]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravita- tion (W. H. Freeman Princeton University Press, United States, 1973)

    1973

  31. [39]

    J. A. Petterson, Magnetic field of a current loop around a Schwarzschild black hole, Phys. Rev. D 10, 3166 (1974)

    1974

  32. [40]

    standard

    I. Wasserman and S. L. Shapiro, Masses, radii, and mag- netic fields of pulsating X-ray sources : is the “standard” model self-consistent ?, Astrophys. J. 265, 1036 (1983)

    1983

  33. [41]

    T. M. Braje and R. W. Romani, Magnetospheric Scat- tering and Emission in Millisecond Pulsars, Astrophys. J. 550, 392 (2001), arXiv:astro-ph/0004407 [astro-ph]

    2001 arXiv

  34. [42]

    This dipole field is identical to those generated by an electric current loop orbiting in the equatorial plane of the Schwarzschild geometry [32, 50, 85]

  35. [43]

    Bakala, E

    P. Bakala, E. ˇSr´ amkov´ a, Z. Stuchl ´ ık, and G. T¨ or¨ ok, On magnetic-field-induced non-geodesic corrections to rela- tivistic orbital and epicyclic frequencies, Classical and Quantum Gravity 27, 045001 (2010)

    2010

  36. [44]

    Urbanec, J

    M. Urbanec, J. C. Miller, and Z. Stuchl ´ ık, Quadrupole moments of rotating neutron stars and strange stars, Monthly Notices of the RAS 433, 1903 (2013), arXiv:1301.5925 [astro-ph.SR]

    2013 arXiv

  37. [45]

    R. C. Tolman, Static solutions of Einstein’s field equa- tions for spheres of fluids, Phys. Rev. 55, 364 (1939)

    1939

  38. [46]

    Jiang and K

    N. Jiang and K. Yagi, Improved analytic modeling of neutron star interiors, Phys. Rev. D 99, 124029 (2019), arXiv:1904.05954 [gr-qc]

    2019 arXiv

  39. [47]

    Stuchl ´ ık and J

    Z. Stuchl ´ ık and J. Vrba, Trapping of null geodesics in slowly rotating extremely compact Tolman VII space- times, European Physical Journal Plus 136, 977 (2021), arXiv:2108.09466 [gr-qc]

    2021 arXiv

  40. [48]

    M. A. Abramowicz, J. C. Miller, and Z. Stuchl ´ ık, Concept of radius of gyration in general relativity, Phys. Rev. D 47, 1440 (1993)

    1993

  41. [49]

    Stuchl ´ ık, S

    Z. Stuchl ´ ık, S. Hled ´ ık, and J. Novotn´ y, General relativis- tic polytropes with a repulsive cosmological constant, Phys. Rev. D 94, 103513 (2016), arXiv:1611.05327 [gr- qc]

    2016 arXiv

  42. [50]

    Novotn´ y, J

    J. Novotn´ y, J. Hlad ´ ık, and Z. Stuchl ´ ık, Polytropic spheres containing regions of trapped null geodesics, Phys. Rev. D 95, 043009 (2017), arXiv:1703.04604 [gr-qc]

    2017 arXiv

  43. [51]

    N. K. Glendenning, ed., Compact stars : nuclear physics, particle physics, and general relativity / Norman K. Glendenning. New York : Springer, 2000. (Astronomy and astrophysics library) (2000)

    2000

  44. [52]

    Bahcall, B

    S. Bahcall, B. W. Lynn, and S. B. Selipsky, Fermion Q- stars, Nuclear Physics B 325, 606 (1989)

    1989

  45. [53]

    Weber, Pulsars as Astrophysical Laboratories for Nu- clear and Particle Physics (CRC Press, 2017)

    F. Weber, Pulsars as Astrophysical Laboratories for Nu- clear and Particle Physics (CRC Press, 2017)

    2017

  46. [54]

    van der Klis, Millisecond Oscillations in X-ray Bina- 38 ries, Annual Review of Astronomy and Astrophysics 38, 717 (2000), arXiv:astro-ph/0001167 [astro-ph]

    M. van der Klis, Millisecond Oscillations in X-ray Bina- 38 ries, Annual Review of Astronomy and Astrophysics 38, 717 (2000), arXiv:astro-ph/0001167 [astro-ph]

    2000 arXiv

  47. [55]

    Ecker and L

    C. Ecker and L. Rezzolla, Impact of large-mass con- straints on the properties of neutron stars, Monthly No- tices of the RAS 519, 2615 (2023), arXiv:2209.08101 [astro-ph.HE]

    2023 arXiv

  48. [56]

    S. B. Popov, Origins of magnetars in binary systems, Astronomical and Astrophysical Transactions 29, 183 (2016), arXiv:1507.08192 [astro-ph.HE]

    2016 arXiv

  49. [58]

    A. N. Aliev and D. V. Galtsov, Radiation from relativistic particles in nongeodesic motion in a strong gravitational field., General Relativity and Gravitation 13, 899 (1981)

    1981

  50. [59]

    Kov´ aˇ r, Z

    J. Kov´ aˇ r, Z. Stuchl ´ ık, and V. Karas, Off-equatorial orbits in strong gravitational fields near compact ob- jects, Classical and Quantum Gravity 25, 095011 (2008), arXiv:0803.3155 [astro-ph]

    2008 arXiv

  51. [60]

    Particles under magnetic attraction, with b > 0, have to follow the counter-rotating off-equatorial orbits with ωφ < 0

  52. [61]

    Bicak, Z

    J. Bicak, Z. Stuchlik, and V. Balek, The Motion of Charged Particles in the Field of Rotating Charged Black Holes and Naked Singularities. I. The General Features of the Radial Motion and the Motion Along the Axis of Symmetry, Bulletin of the Astronomical Institutes of Czechos...

    1989

  53. [62]

    Balek, J

    V. Balek, J. Bicak, and Z. Stuchlik, The Motion of the Charged Particles in the Field of Rotating Charged Black Holes and Naked Singularities. II. The Motion in the Equatorial Plane, Bulletin of the Astronomical Institutes of Czechoslovakia 40, 133 (1989)

    1989

  54. [63]

    J. E. Gunn and J. P. Ostriker, Magnetic Dipole Radiation from Pulsars, Nature (London) 221, 454 (1969)

    1969

  55. [64]

    R. A. Chevalier and C. Fransson, Circumstellar matter and the nature of the SN1987A progenitor star, Nature (London) 328, 44 (1987)

    1987

  56. [65]

    J. B. Climent, J. C. Guirado, M. P´ erez-Torres, J. M. Marcaide, and L. Pe˜ na-Mo˜ nino, Evidence for a radiation belt around a brown dwarf, Science 381, 1120 (2023), arXiv:2303.06453 [astro-ph.SR]

    2023 arXiv

  57. [66]

    V. P. Frolov and A. A. Shoom, Motion of charged parti- cles near a weakly magnetized Schwarzschild black hole, Phys. Rev. D 82, 084034 (2010), arXiv:1008.2985 [gr-qc]

    2010 arXiv

  58. [67]

    R. C. Duncan and C. Thompson, Formation of Very Strongly Magnetized Neutron Stars: Implications for Gamma-Ray Bursts, Astrophysical Journal Letters 392, L9 (1992)

    1992

  59. [68]

    V. V. Usov, Millisecond pulsars with extremely strong magnetic fields as a cosmological source of γ-ray bursts, Nature (London) 357, 472 (1992)

    1992

  60. [69]

    L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-relativistic Theory , 3rd ed., Course of Theoretical Physics, Vol. 3 (Pergamon Press, London, 1977)

    1977

  61. [70]

    L. B. Loeb, Science 124, 35 (1956), https://www.science.org/doi/pdf/10.1126/science.124.3210.35.a

    1956 doi

  62. [71]

    Kimura and P

    K. Kimura and P. J. Morrison, On energy conservation in extended magnetohydrodynamics, Physics of Plasmas 21, 082101 (2014), arXiv:1406.2745 [physics.plasm-ph]

    2014 arXiv

  63. [72]

    Comisso and F

    L. Comisso and F. A. Asenjo, Thermal-Inertial Effects on Magnetic Reconnection in Relativistic Pair Plasmas, Phys. Rev. Lett. 113, 045001 (2014), arXiv:1402.1115 [physics.plasm-ph]

    2014 arXiv

  64. [73]

    Kawazura, Modification of magnetohydrodynamic waves by the relativistic Hall effect, Phys

    Y. Kawazura, Modification of magnetohydrodynamic waves by the relativistic Hall effect, Phys. Rev. E 96, 013207 (2017), arXiv:1706.07077 [physics.plasm-ph]

    2017 arXiv

  65. [74]

    Yoshino, M

    S. Yoshino, M. Hirota, and Y. Hattori, Applicability cri- teria of proper charge neutrality and special relativis- tic MHD models extended by two-fluid effects, arXiv e-prints , arXiv:2410.03317 (2024), arXiv:2410.03317 [physics.plasm-ph]

    2024 arXiv

  66. [75]

    J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999)

    1999

  67. [76]

    Poisson, The Motion of Point Particles in Curved Spacetime, Living Reviews in Relativity 7, 6 (2004), arXiv:gr-qc/0306052 [gr-qc]

    E. Poisson, The Motion of Point Particles in Curved Spacetime, Living Reviews in Relativity 7, 6 (2004), arXiv:gr-qc/0306052 [gr-qc]

    2004 arXiv

  68. [77]

    J. S. Santos, V. Cardoso, and J. Nat´ ario, Electromag- netic radiation reaction and energy extraction from black holes: The tail term cannot be ignored, Phys. Rev. D 107, 064046 (2023), arXiv:2303.03411 [gr-qc]

    2023

  69. [78]

    J. S. Santos, V. Cardoso, and J. Nat´ ario, Radiation reac- tion in weakly magnetized black holes: Can the tail term be ignored in the strong field regime?, Phys. Rev. D 109, 124032 (2024), arXiv:2404.02195 [gr-qc]

    2024 arXiv

  70. [79]

    Tursunov, M

    A. Tursunov, M. Zajaˇ cek, A. Eckart, M. Koloˇ s, S. Britzen, Z. Stuchl ´ ık, B. Czerny, and V. Karas, Ef- fect of Electromagnetic Interaction on Galactic Cen- ter Flare Components, Astrophys. J. 897, 99 (2020), arXiv:1912.08174 [astro-ph.GA]

    2020 arXiv

  71. [80]

    The tail term enters the play for extremely compact stars having a radius at R <3M

  72. [81]

    Koloˇ s, M

    M. Koloˇ s, M. Shahzadi, and A. Tursunov, Charged particle dynamics in parabolic magnetosphere around Schwarzschild black hole, European Physical Journal C 83, 323 (2023), arXiv:2304.13603 [gr-qc]

    2023 arXiv

  73. [82]

    For the possible role of the tail term in the RR force see [27]

  74. [83]

    An epicyclic harmonic motion is, of course, possible in a sufficiently small vicinity of stable circular orbits also in the chaotic regime of the motion

  75. [84]

    Dadhich, R

    N. Dadhich, R. Maartens, P. Papadopoulos, and V. Reza- nia, Black holes on the brane, Physics Letters B 487, 1 (2000), arXiv:hep-th/0003061 [hep-th]

    2000 arXiv

  76. [85]

    Kotrlov´ a, Z

    A. Kotrlov´ a, Z. Stuchl ´ ık, and G. T¨ or¨ ok, Quasiperiodic oscillations in a strong gravitational field around neutron stars testing braneworld models, Classical and Quantum Gravity 25, 225016 (2008), arXiv:0812.0720 [astro-ph]

    2008 arXiv

  77. [86]

    Stuchl ´ ık and M

    Z. Stuchl ´ ık and M. Koloˇ s, Acceleration of the charged particles due to chaotic scattering in the combined black hole gravitational field and asymptotically uniform mag- netic field, European Physical Journal C 76, 32 (2016), arXiv:1511.02936 [gr-qc]

    2016 arXiv

  78. [87]

    Tursunov, Z

    A. Tursunov, Z. Stuchl ´ ık, M. Koloˇ s, N. Dadhich, and B. Ahmedov, Supermassive Black Holes as Possible Sources of Ultrahigh-energy Cosmic Rays, Astrophys. J. 895, 14 (2020), arXiv:2004.07907 [astro-ph.HE]

    2020 arXiv

  79. [88]

    Carter, Black hole equilibrium states., in Black Holes (Les Astres Occlus) (1973) pp

    B. Carter, Black hole equilibrium states., in Black Holes (Les Astres Occlus) (1973) pp. 57–214

    1973

  80. [89]

    Stuchlik, The Motion of Test Particles in Black-Hole Backgrounds with Non-Zero Cosmological Constant, Bul- letin of the Astronomical Institutes of Czechoslovakia34, 129 (1983)

    Z. Stuchlik, The Motion of Test Particles in Black-Hole Backgrounds with Non-Zero Cosmological Constant, Bul- letin of the Astronomical Institutes of Czechoslovakia34, 129 (1983)

    1983

  81. [90]

    G. V. Kraniotis, Frame dragging and bending of light in Kerr and Kerr (anti) de Sitter spacetimes, Classical and Quantum Gravity 22, 4391 (2005), arXiv:gr-qc/0507056 [gr-qc]. 39

    2005 arXiv

  82. [91]

    G. V. Kraniotis, Gravitational redshift/blueshift of light emitted by geodesic test particles, frame-dragging and pericentre-shift effects, in the Kerr-Newman-de Sit- ter and Kerr-Newman black hole geometries, European Physical Journal C 81, 147 (2021)

    2021

  83. [92]

    Preti, On charged particle orbits in dipole magnetic fields around Schwarzschild black holes, Classical and Quantum Gravity 21, 3433 (2004)

    G. Preti, On charged particle orbits in dipole magnetic fields around Schwarzschild black holes, Classical and Quantum Gravity 21, 3433 (2004)

    2004

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.