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Nonlinear electrodynamics creates forbidden regions that reverse free-fall before tidal forces can diverge in multi-horizon black holes.

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2026-07-11 15:54 UTC pith:2WSPAO5D

load-bearing objection Solid classical-GR calculation on Gao multi-horizon NED metrics: multiple tidal zeros, exterior forbidden regions for radial free-fallers, and a clean critical-charge hierarchy; scope is narrow but the math holds. the 2 major comments →

arxiv 2607.04642 v2 pith:2WSPAO5D submitted 2026-07-06 gr-qc

Beyond the Bounce: Multiple Tidal Sign Reversals and Turning-Point Bifurcations in Multi-Horizon Black Holes

Mohammad Ali S. Afshar , J. Sadeghi This is my paper
classification gr-qc
keywords tidal forcemulti-horizon black holesnonlinear electrodynamicsgeodesic deviationbounce-back pointsforbidden regionssuper-extremal charge
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper studies how neutral particles that fall straight in from rest behave near black holes that have three or four horizons, solutions that appear when Einstein gravity is coupled to nonlinear electrodynamics. It shows that the nonlinear field produces multiple places where radial and angular tidal forces reverse from stretching to compression and back, unlike the single transition of Reissner–Nordström. More importantly, the radial motion develops classically forbidden intervals bounded by bounce-back points; particles on the trajectories considered reverse direction before they reach the domain where those tidal forces become infinite. In the super-extremal charge window the forbidden interval can even sit outside the event horizon, so particles released far away never cross it. The critical charges at which zeros, extra horizons, and bounce points first appear obey a fixed hierarchy, so the tidal structure changes before the horizon count does. The result matters because it shows a way for nonlinear electromagnetism to protect free-falling matter from spaghettification and even from capture without removing the central singularity.

Core claim

For neutral particles released from rest at large fixed radius in the three- and four-horizon NED black-hole solutions, the radial equation of motion develops classically forbidden regions bounded by bounce-back points. These regions prevent the particles from entering the spacetime domain in which the radial and angular tidal forces diverge. The same solutions admit a super-extremal regime in which the forbidden region can extend outside the event horizon. Critical charge values at which tidal-force zeros, additional horizons, and bounce-back points appear satisfy the hierarchical ordering q_rad < q_ang < q_H < q_TP for both the three- and four-horizon families.

What carries the argument

The radial energy equation (dr/dτ)^{2} = f(b) − f(r) together with the tidal eigenvalues η_radial = −½ f''(r) and η_angular = −f'(r)/(2r). Non-monotonicity of the NED-corrected metric function f(r) produces extra real roots that define both the bounce-back points and the multiple zero-crossings of the tidal components.

Load-bearing premise

Every dynamical conclusion is drawn only for neutral particles that fall radially from rest at one fixed large starting radius; the paper does not show that the forbidden-region barrier or the charge hierarchy survive for spinning, charged, or non-radial trajectories.

What would settle it

Compute the radial effective potential for the same NED metrics with nonzero angular momentum L and check whether a forbidden interval still appears that keeps an infalling particle outside the divergent-tidal domain for the same charge windows reported in Tables 1 and 2.

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

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper studies radial free-fall of neutral test particles and the associated tidal forces in the three- and four-horizon black-hole solutions of Einstein gravity coupled to nonlinear electrodynamics constructed by Gao. Using the standard radial equation (dr/d au)^{2} = f(b) − f(r) and the tidal eigenvalues η_radial = −½f″, η_angular = −f′/(2r), the authors show that the higher-order inverse-power terms in the metric functions produce multiple zero crossings of both tidal components and, above critical charges, classically forbidden intervals bounded by bounce-back points. For the restricted class of trajectories released from rest at fixed large b, these forbidden regions prevent the particle from reaching the domain where the tidal forces diverge; in a super-extremal window the outer turning point can even lie outside the event horizon. Numerical root-finding further reveals a hierarchical ordering of the critical charges at which radial zeros, angular zeros, additional horizons and turning points successively appear (q_rad < q_ang < q_H < q_TP). The results are presented for representative values of the NED couplings and are summarized in two extensive tables.

Significance. If the reported hierarchy and the protective role of the forbidden regions survive under modest generalizations of the initial conditions, the work supplies a concrete, observationally relevant signature that distinguishes multi-horizon NED geometries from both Schwarzschild and Reissner–Nordström spacetimes. The explicit demonstration that a classical singularity can remain kinematically inaccessible without being removed is of independent theoretical interest. The calculations themselves are standard and transparent; the numerical tables are internally consistent and the metric functions match the cited construction. The principal limitation is the restriction to a single, highly symmetric class of trajectories, which the authors repeatedly flag.

major comments (2)
  1. All dynamical conclusions (forbidden-region barrier, avoidance of divergent tides, super-extremal non-capture, and the hierarchy of Eq. (26)) rest exclusively on neutral radial free-fall from rest at fixed b = 100 M (Eq. (9) and Secs. 4.2–4.3, 5.1–5.2). The paper does not demonstrate that the same qualitative features persist for nonzero angular momentum, nonzero initial radial velocity, or charged test particles. While the restriction is repeatedly acknowledged, a short exploration of at least one neighboring class of trajectories (e.g., small L or E > √f(b)) would substantially strengthen the central claim that the NED field generically protects against divergent tides.
  2. The hierarchical ordering q_rad < q_ang < q_H < q_TP is established only for two fixed sets of NED couplings (α₂ = −0.004 for three horizons; α₂ = −0.0004, α₃ = 6.38736 × 10⁻⁷ for four horizons). Tables 1–2 therefore leave open whether the ordering is robust under variation of the free parameters. A brief scan over a modest range of α_i would clarify whether the sequence is a structural feature of the multi-horizon NED family or an artifact of the chosen numerical values.
minor comments (4)
  1. Several figure captions contain typographical inconsistencies (e.g., “r·2 function”, “VI-Horizon” instead of “IV-Horizon”, and repeated “ηRadial” labels on angular-force plots). These should be corrected for clarity.
  2. The geodesic-deviation solutions (21)–(22) and (24)–(25) are written but never used or plotted; either a short discussion of their physical content or their removal would improve focus.
  3. The phrase “preventing spaghettification” appears in the abstract and discussion; given the trajectory restriction it should be qualified more carefully (e.g., “along the trajectories considered here”).
  4. Self-citations [51–66] occupy a large fraction of the reference list; a few additional independent works on multi-horizon NED or tidal forces in regular black holes would better situate the contribution.

Circularity Check

0 steps flagged

No significant circularity: hierarchy and forbidden-region claims are numerical outputs of standard root-finding on external metrics, not inputs or self-fitted predictions.

full rationale

The derivation chain is self-contained and non-circular. Metric functions (17) and (23) are taken from the external reference Gao [67]; the tidal eigenvalues (7)–(8) and radial equation (9) are textbook projections of the Riemann tensor and Killing energy for the static spherical line element. Critical charges q_rad, q_ang, q_H, q_TP listed in Tables 1–2 and ordered in (26) are obtained by numerical root-finding on f(r)=0, f'(r)=0, f''(r)=0 and f(b)-f(r)=0 for fixed α_i, M, b=100; they are not fitted parameters that are later re-labeled as predictions. Self-citations [51–66] concern unrelated thermodynamic or WGC topics of the same group and are never invoked as premises for the tidal hierarchy or the existence of bounce-back points. No uniqueness theorem, ansatz, or definitional identity is smuggled in. The repeated qualifier “for the class of trajectories considered in this work” correctly limits the scope but does not create circularity. Score 0 is therefore required.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The paper inherits the multi-horizon NED metrics from Gao and applies standard GR geodesic-deviation machinery. Load-bearing free choices are the truncation of the NED series, the hand-picked coupling constants, and the fixed release radius b=100M that define the trajectory class. No new physical entities are postulated; the “forbidden region” and “bounce-back points” are kinematic features of the radial equation, not new fields or particles.

free parameters (4)
  • α₂ (three-horizon) = -0.004
    Coupling constant fixed by hand at −0.004 to produce three horizons; all critical-q thresholds and figures depend on this choice.
  • α₂, α₃ (four-horizon) = α₂=-0.0004, α₃=6.38736e-7
    α₂=−0.0004 and α₃=6.38736×10⁻⁷ chosen so the four-horizon configuration is comparable to the three-horizon case; hierarchy thresholds shift with these values.
  • release radius b = 100 M
    All radial-motion and forbidden-region statements use particles released from rest at b=100M; the super-extremal “charge window” is defined relative to this b.
  • mass M = 1
    Set to 1 without loss of generality for numerical scans; critical charges are quoted in units of M.
axioms (4)
  • domain assumption Einstein gravity coupled to the infinite-series NED Lagrangian of Gao yields the exact static spherical metrics (17) and (23) with the stated truncations α₃=4α₂², …
    Entire geometry and all subsequent roots are taken from ref. [67]; no independent derivation is supplied.
  • standard math Tidal forces for a radially freely falling observer are exactly η_radial=−½f″(r) and η_angular=−f′(r)/(2r) in the orthonormal tetrad (3)–(6).
    Standard geodesic-deviation projection for static spherical metrics; used throughout Secs. 2 and 4–5.
  • ad hoc to paper Only neutral test particles released from rest at r=b are considered; angular momentum and charge of the test particle are set to zero.
    Explicitly restricts the trajectory class that underpins every claim about forbidden regions and protection from divergent tides (Secs. 2.3, 4.2, 5.1).
  • domain assumption Classical geodesic motion remains valid through the intermediate-horizon region; mass-inflation and quantum back-reaction at Cauchy-like horizons can be set aside for the bounce interpretation.
    Paper notes mass-inflation risk but still interprets bounce-back as a classical turning point in the same manifold (Sec. 4.2 items i–ii).

pith-pipeline@v1.1.0-grok45 · 28232 in / 3579 out tokens · 33056 ms · 2026-07-11T15:54:38.413980+00:00 · methodology

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read the original abstract

We investigate the radial motion and tidal forces experienced by neutral test particles in multi-horizon black hole solutions arising from Einstein gravity coupled to nonlinear electrodynamics (NED). Focusing on the three- and four-horizon configurations, we examine how nonlinear electromagnetic corrections modify the causal structure, radial geodesic motion, and tidal-force profiles in comparison with the Schwarzschild and Reissner-Nordstrom (R-N) spacetimes. Our analysis shows that the NED field gives rise to multiple zero crossings in both the radial and angular tidal-force components, leading to successive transitions between stretching and compressive tidal regimes. More importantly, the radial equation of motion contains classically forbidden regions bounded by bounce-back points. For the class of trajectories considered in this work, these forbidden regions prevent particles from entering the spacetime domain where the tidal forces become divergent. In the super-extremal regime admitted by these solutions, the forbidden region may extend beyond the event horizon, preventing particles released from rest at sufficiently large distances from crossing the horizon. We further identify a systematic ordering of the critical charge values associated with the appearance of tidal-force zero crossings, additional horizons, and bounce-back points. For both the three- and four-horizon configurations, these critical values satisfy a hierarchical ordering, indicating that changes in the tidal-force structure precede the corresponding modifications of the horizon configuration. These results demonstrate that nonlinear electrodynamics can substantially modify the classical dynamics of neutral particles in multi-horizon black hole spacetimes through the combined effects of forbidden regions, multiple tidal transitions, and changes in the horizon structure.

Figures

Figures reproduced from arXiv: 2607.04642 by J. Sadeghi, Mohammad Ali S. Afshar.

Figure 1
Figure 1. Figure 1: Fig. 1: Metric function with [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: r ·2 function with M = 1 and different q for R-N and Schwarzschild Black hole. once the physical instability of the Cauchy horizon is taken into account, together with the fact that Rstop always lies inside the inner horizon, this portion of the maximal analytic extension is generally regarded as physically inaccessible [9]. Nevertheless, this characteristic feature of the R-N so￾lution illustrates the inf… view at source ↗
Figure 3
Figure 3. Figure 3: r ·2 function with α2 = −0.004, b = 100, M = 1, q = 0.8222 for III-Horizon structure of NED Black hole. shows that, although the NED corrections generate an additional intermediate horizon for q & 0.75, the radial dynamics remain qualitatively Schwarzschild-like over this interval, indicating that the gravitational contri￾bution still dominates the particle motion. The ap￾pearance of nonzero extrema nevert… view at source ↗
Figure 5
Figure 5. Figure 5: r ·2 function with α2 = −0.004, b = 100, M = 1 for 5a: q = 0.85, 5b: q = 0.92 , 5c: q = 1 in III-Horizon structure of NED Black hole. Another notable feature, visible in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: r ·2 function with α2 = −0.004, b = 100, M = 1 for 6a: q = 0.85, 6b: set of behaviors for different charges in III-Horizon structure of NED Black hole. b = 100M), the outer turning point continues to move outward until it eventually coincides with the particle’s release position (r = b). Beyond this point, no addi￾tional turning point exists between the release position and the event horizon, allowing the … view at source ↗
Figure 7
Figure 7. Figure 7: ηRadial function with α2 = −0.004, b = 100, M = 1, q = 0.547 for III-Horizon structure of NED Black hole. Beyond the first threshold, the radial tidal force devel￾ops two zero crossings.For charge values corresponding to the single-horizon configuration, both zero crossings are located inside the event horizon. After the interme￾diate and inner horizons appear, the two zero crossings lie initially between … view at source ↗
Figure 8
Figure 8. Figure 8 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: ηRadial function with α2 = −0.004, b = 100, M = 1, q = 0.85, in III-Horizon structure of NED Black hole. viously, neutral particles released from rest at suffi￾ciently large distances cannot penetrate the classically forbidden region. Instead, they reach its outer bound￾ary (approximately r ≃ 2.0 for a particle released from b = 100), where they reverse their motion and move outward. Consequently, such par… view at source ↗
Figure 10
Figure 10. Figure 10: ηRadial function with α2 = −0.004, b = 100, M = 1 for 10a: q = 2, 10b: set of behaviors for different charges in III-Horizon structure of NED Black hole. range of charge values reveals a behavior that dif￾fers qualitatively from both the Schwarzschild and RN spacetimes while exhibiting several similarities to the radial tidal force in the present NED solution. As for the radial component, three distinct r… view at source ↗
Figure 11
Figure 11. Figure 11: ηangular function with α2 = −0.004, b = 100, M = 1, q = 0.623, in III-Horizon structure of NED Black hole [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: ηangular function with α2 = −0.004, b = 100, M = 1 for 13a: q = 0.85, 13b: q = 1 in III-Horizon structure of NED Black hole. from the exterior first experiences a compressive an￾gular force after crossing the event horizon. At r ≈ 0.713M, the force changes sign and becomes stretch￾ing. The subsequent evolution, however, differs quali￾tatively from that of the Schwarzschild and R-N space￾times. The region … view at source ↗
Figure 12
Figure 12. Figure 12: ηRadial function with α2 = −0.004, b = 100, M = 1 for 11a: q = 0.624, 11b: q = 0.75, in III￾Horizon structure of NED Black hole. returning to compression and eventually diverging as the singularity is approached ( [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 14
Figure 14. Figure 14 [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
Figure 16
Figure 16. Figure 16: r ·2 function with α3 = 6.38736 × 10−7 , α2 = −0.004, b = 100, M = 1, q = 0.85 in VI￾Horizon structure of NED Black hole. solution, the four-horizon geometry continues to ad￾mit black hole solutions beyond the R-N extremality bound. In this case as well, in the super-extremal regime, the classically forbidden region expands out￾ward and extends beyond the event horizon. Conse￾quently, particles released f… view at source ↗
Figure 15
Figure 15. Figure 15: r ·2 function with α3 = 6.38736 × 10−7 , α2 = −0.004, b = 100, M = 1 for 6a: q = 0.424, 6b: q = 0.53 in VI-Horizon structure of NED Black hole. caution. Unlike the RN case, the bounce-back point re￾mains located very close to the innermost horizon and exhibits only a very weak dependence on the black hole charge. Furthermore, although this point is apparently accessible from a mathematical point of view, … view at source ↗
Figure 17
Figure 17. Figure 17: r ·2 function with α3 = 6.38736 × 10−7 , α2 = −0.004, b = 100, M = 1, q = 2 in VI￾Horizon structure of NED Black hole. • Schwarzschild-Like Region:q ≤ 0.4244. • New Behavioral Region: 0.4244 < q < 0.561. • R-N Like Protected Region: q ≥ 0.561. It is worth emphasizing that the phrase ’with slight deviation’ has a different interpretation in each of the three behavioral regimes. In all these configurations,… view at source ↗
Figure 18
Figure 18. Figure 18: ηRadial function with α3 = 6.38736 × 10−7 , α2 = −0.004, b = 100, M = 1 for 18a: q = 0.373, 18b: q = 0.49, 18c: q = 0.75 in VI-Horizon structure of NED Black hole. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_18.png] view at source ↗
Figure 20
Figure 20. Figure 20: 20a: ηradial and 20b: ηangular function set of behaviors for different charges in III-Horizon struc￾ture of NED Black hole. 5.3 Geodesic Deviation Equations Given the general form of the metric function (1) and energy, by substituting 7 and 8 into 2 and solving the differential equations, the geodesic deviation for the horizon form of the 4 NED black holes will be obtained as follows: κ(r) = − 2M b + q 2 … view at source ↗
Figure 19
Figure 19. Figure 19: 19a: ηradial and 19b: ηangular function with α3 = 6.38736×10−7 , α2 = −0.004, b = 100, M = 1, q = 2 for VI-Horizon structure of NED Black hole. can have a comprehensive look at the behavior of the tidal force components in the 4-horizon structure for different values of q [PITH_FULL_IMAGE:figures/full_fig_p015_19.png] view at source ↗

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Reference graph

Works this paper leans on

67 extracted references · 1 canonical work pages

  1. [1]

    Q in the Solar System

    Goldreich P, Soter S. Q in the Solar System. icarus. 1966 Jan 1;5(1-6):375-89

    1966

  2. [2]

    Melting of Io by tidal dissipation

    Peale SJ, Cassen P, Reynolds RT. Melting of Io by tidal dissipation. Science. 1979 Mar 2;203(4383):892-4

    1979

  3. [3]

    Tidal forces in Kot- tler spacetimes

    Vandeev VP, Semenova AN. Tidal forces in Kot- tler spacetimes. The European Physical Journal C. 2021 Jul;81(7):610. 17

    2021

  4. [4]

    Tidal forces in Majumdar-Papapetrou spacetimes

    Albacete E, Richartz M. Tidal forces in Majumdar-Papapetrou spacetimes. Universe. 2024 Jan 31;10(2):62., arXiv:2402.01634 [gr-qc]

    Pith/arXiv arXiv 2024

  5. [5]

    Tidal forces in parametrized spacetime: Rezzolla-Zhidenko parametrization

    Toshmatov B, Ahmedov B. Tidal forces in parametrized spacetime: Rezzolla-Zhidenko parametrization. Physical Review D. 2023 Oct 15;108(8):084035

    2023

  6. [6]

    Relativistic tidal ten- sor: General solutions for stationary axisym- metric spacetimes and the Hills mass of naked singularities

    Xin W, Mummery A. Relativistic tidal ten- sor: General solutions for stationary axisym- metric spacetimes and the Hills mass of naked singularities. Physical Review D. 2026 Feb 15;113(4):044036

    2026

  7. [7]

    Introducing Einstein’s rel- ativity: a deeper understanding

    d’Inverno R, Vickers J. Introducing Einstein’s rel- ativity: a deeper understanding. Oxford Univer- sity Press; 2022. Thorne KS, Misner CW, Wheeler JA. Gravita- tion. San Francisco: Freeman; 2000

    2022

  8. [8]

    General relativity: an introduction for physicists

    Hobson MP, Efstathiou GP, Lasenby AN. General relativity: an introduction for physicists. Cam- bridge university press; 2006 Feb 2. Wald RM. General relativity. University of Chicago press; 2010 May 15

    2006

  9. [9]

    Tidal forces in Reissner–Nordström space- times

    Crispino LC, Higuchi A, Oliveira LA, de Oliveira ES. Tidal forces in Reissner–Nordström space- times. The European Physical Journal C. 2016 Mar;76(3):168. arXiv:1602.07232 [gr-qc]

    Pith/arXiv arXiv 2016

  10. [10]

    Tidal forces around the Letelier- Alencar cloud of strings black hole

    Silva MV, Crispim TM, Landim RR, Olmo GJ, Gómez DS. Tidal forces around the Letelier- Alencar cloud of strings black hole. Physical Re- view D. 2026 Mar 15;113(6):064052

    2026

  11. [11]

    Geodesic deviation in the q-metric

    Idrissov A, Boshkayev K, Dialektopoulos KF, Urazalina A, Utepova D. Geodesic deviation in the q-metric. The European Physical Journal C. 2025 Mar 20;85(3):319

    2025

  12. [12]

    Free-falling test particles in a charged Kalb-Ramond black hole: Gravitational Doppler effect and tidal forces

    Cordeiro DS, Junior EL, Junior JT, Lobo FS, Rodrigues ME, Rubiera-Garcia D, da Silva LF, Vieira HA. Free-falling test particles in a charged Kalb-Ramond black hole: Gravitational Doppler effect and tidal forces. Physical Review D. 2025 Nov 15;112(10):104018

    2025

  13. [13]

    Graviton noise on tidal forces and geodesic congruences

    Cho HT, Hu BL. Graviton noise on tidal forces and geodesic congruences. Physical Review D. 2023 Apr 15;107(8):084005

    2023

  14. [14]

    Exploring tidal force effects and shadow constraints for Schwarzschild- like black hole in Starobinsky–Bel-Robinson grav- ity

    Arora D, Molla NU, Chaudhary H, Debnath U, Atamurotov F, Mustafa G. Exploring tidal force effects and shadow constraints for Schwarzschild- like black hole in Starobinsky–Bel-Robinson grav- ity. The European Physical Journal C. 2023 Nov 3;83(11):995

    2023

  15. [15]

    Tidal forces in collapsing compact objects

    Joshi AB, Dey D, Joshi PS, Tank VR. Tidal forces in collapsing compact objects. Physical Review D. 2024 Dec 15;110(12):124066

    2024

  16. [16]

    Tidal effects in 4D Ein- stein–Gauss–Bonnet black hole spacetime

    Li J, Chen S, Jing J. Tidal effects in 4D Ein- stein–Gauss–Bonnet black hole spacetime. The European Physical Journal C. 2021 Jul;81(7):590

    2021

  17. [17]

    Tidal effects based on a GUP-induced effective metric

    Hong ST, Kim YW, Park YJ. Tidal effects based on a GUP-induced effective metric. Com- munications in Theoretical Physics. 2024 Sep 1;76(9):095402

    2024

  18. [18]

    Geodesic completeness, curva- ture singularities and infinite tidal forces

    Zhang X, Gao S. Geodesic completeness, curva- ture singularities and infinite tidal forces. Chinese Physics C. 2025 Jul 7

    2025

  19. [19]

    Tidal stretching and compression in black bounce backgrounds

    Crispim TM, Silva MV, Alencar G, Gómez DS. Tidal stretching and compression in black bounce backgrounds. The European Physical Journal C. 2025 Oct 22;85(10):1186

    2025

  20. [20]

    Tidal forces in dirty black hole spacetimes

    Lima Junior HC, Corrêa MM, Macedo CF, Crispino LC. Tidal forces in dirty black hole spacetimes. The European Physical Journal C. 2022 May 24;82(5):479

    2022

  21. [21]

    Tidal forces in Kiselev black hole

    Shahzad MU, Jawad A. Tidal forces in Kiselev black hole. The European Physical Journal C. 2017 Jun;77(6):372

    2017

  22. [22]

    Tidal forces in the charged Hayward black hole spacetime

    Lima HC, Crispino LC. Tidal forces in the charged Hayward black hole spacetime. Interna- tional Journal of Modern Physics D. 2020 Aug 7;29(11):2041014

    2020

  23. [23]

    Geodesic deviation, Ray- chaudhuri equation, and tidal forces in modified gravity<? format?> with an arbitrary curvature- matter coupling

    Harko T, Lobo FS. Geodesic deviation, Ray- chaudhuri equation, and tidal forces in modified gravity<? format?> with an arbitrary curvature- matter coupling. Physical Review D—Particles, Fields, Gravitation, and Cosmology. 2012 Dec 15;86(12):124034

    2012

  24. [24]

    Tidal effects in Schwarzschild black hole in holographic mas- sive gravity

    Hong ST, Kim YW, Park YJ. Tidal effects in Schwarzschild black hole in holographic mas- sive gravity. Physics Letters B. 2020 Dec 10;811:135967

    2020

  25. [25]

    Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type f (Q, T) gravity

    Yang JZ, Shahidi S, Harko T, Liang SD. Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type f (Q, T) gravity. The European Physical Journal C. 2021 Feb;81(2):111

    2021

  26. [26]

    Fresh look at the effects of gravitational tidal forces on a freely-falling quantum particle

    Hammad F, Sadeghi P, Fleury N, Leblanc A. Fresh look at the effects of gravitational tidal forces on a freely-falling quantum particle. Inter- national Journal of Modern Physics D. 2022 Jan 30;31(01):2150121

    2022

  27. [27]

    Geodesic deviation on symmetry axis in Taub–NUT metric

    Vandeev VP, Semenova AN. Geodesic deviation on symmetry axis in Taub–NUT metric. Interna- tional Journal of Modern Physics D. 2022 Nov 20;31(15):2250108

    2022

  28. [28]

    Tidal forces in f (R) theories of gravity

    Lde la Cruz-Dombriz Á, Dunsby PK, Busti VC, Kandhai S. Tidal forces in f (R) theories of gravity. Physical Review D. 2014 Mar 15;89(6):064029. 18

    2014

  29. [29]

    Tidal Forces in Dyonic Reissner-Nördstrom Black Hole

    Sharif M, Kousar L. Tidal Forces in Dyonic Reissner-Nördstrom Black Hole. Communications in Theoretical Physics. 2018 Mar 1;69(3):257

    2018

  30. [30]

    Curvature singularities, tidal forces and the viability of Pala- tini f (R) gravity

    Barausse E, Sotiriou TP, Miller JC. Curvature singularities, tidal forces and the viability of Pala- tini f (R) gravity. Classical and Quantum Gravity. 2008 May 21;25(10):105008

    2008

  31. [31]

    On- axis tidal forces in Kerr spacetime

    Lima Junior HC, Crispino LC, Higuchi A. On- axis tidal forces in Kerr spacetime. The European Physical Journal Plus. 2020 Mar 30;135(3):334

    2020

  32. [32]

    Tidal forces in Kerr-AdS and Grey galax- ies

    Balivada A, Ranjan Padhi P, Virmani A. Tidal forces in Kerr-AdS and Grey galax- ies. Classical and Quantum Gravity. 2024 Jun 20;41(12):125008

    2024

  33. [33]

    Tidal-disruption rate of stars by spin- ning supermassive black holes

    Kesden M. Tidal-disruption rate of stars by spin- ning supermassive black holes. Physical Review D—Particles, Fields, Gravitation, and Cosmol- ogy. 2012 Jan 15;85(2):024037

    2012

  34. [34]

    Ultraviolet de- tection of the tidal disruption of a star by a su- permassive black hole

    Gezari S, Martin DC, Milliard B, Basa S, Halpern JP, Forster K, Friedman PG, Morrissey P, Neff SG, Schiminovich D, Seibert M. Ultraviolet de- tection of the tidal disruption of a star by a su- permassive black hole. The Astrophysical Journal Letters. 2006 Dec 10;653(1):L25-8

    2006

  35. [35]

    Optical discovery of probable stellar tidal dis- ruption flares

    Van Velzen S, Farrar GR, Gezari S, Morrell N, Zaritsky D, Östman L, Smith M, Gelfand J, Drake AJ. Optical discovery of probable stellar tidal dis- ruption flares. The Astrophysical Journal. 2011 Nov 10;741(2):73

    2011

  36. [36]

    J. A. Wheeler, Mechanisms for jets, in Proceed- ings of a Study Week on Nuclei of Galaxies, ed. by D. J. K. O’Connell,p.539 (1971)

    1971

  37. [37]

    Observa- tion of gravitational waves from a binary black hole merger

    Abbott BP, Abbott R, Abbott TD, Abernathy MR, Acernese F, Ackley K, Adams C, Adams T, Addesso P, Adhikari RX, Adya VB. Observa- tion of gravitational waves from a binary black hole merger. Physical review letters. 2016 Feb 12;116(6):061102

    2016

  38. [38]

    GW170104: ob- servation of a 50-solar-mass binary black hole co- alescence at redshift 0.2

    Abbott BP, Abbott R, Abbott TD, Acernese F, Ackley K, Adams C, Adams T, Addesso P, Ad- hikari RX, Adya VB, Affeldt C. GW170104: ob- servation of a 50-solar-mass binary black hole co- alescence at redshift 0.2. Physical review letters. 2017 Jun 2;118(22):221101

    2017

  39. [39]

    The noise of gravitons

    Parikh M, Wilczek F, Zahariade G. The noise of gravitons. International Journal of Modern Physics D. 2020 Oct 21;29(14):2042001

    2020

  40. [40]

    Quantum me- chanics of gravitational waves

    Parikh M, Wilczek F, Zahariade G. Quantum me- chanics of gravitational waves. Physical Review Letters. 2021 Aug 20;127(8):081602

    2021

  41. [41]

    Signatures of the quantization of gravity at gravitational wave detectors

    Parikh M, Wilczek F, Zahariade G. Signatures of the quantization of gravity at gravitational wave detectors. Physical Review D. 2021 Aug 15;104(4):046021

    2021

  42. [42]

    Tidal disruption of stars by supermas- sive black holes: Status of observations

    Komossa S. Tidal disruption of stars by supermas- sive black holes: Status of observations. Journal of High Energy Astrophysics. 2015 Sep 1;7:148-57

    2015

  43. [43]

    Tidal Disruption of Stars by Supermassive Black Holes and Naked Singulari- ties with Scalar Hair

    Andre E, Tsirulev A. Tidal Disruption of Stars by Supermassive Black Holes and Naked Singulari- ties with Scalar Hair. Physics of Atomic Nuclei. 2024 Feb;87(1):56-64

    2024

  44. [44]

    Tidal forces in naked singularity backgrounds

    Goel A, Maity R, Roy P, Sarkar T. Tidal forces in naked singularity backgrounds. Physical Review D. 2015 May 15;91(10):104029

    2015

  45. [45]

    Roche limit and stellar disruption in the Simpson–Visser spacetime

    Silva MV. Roche limit and stellar disruption in the Simpson–Visser spacetime. arXiv preprint arXiv:2601.16082. 2026 Jan 22

    Pith/arXiv arXiv 2026

  46. [46]

    Relativistic tidal divergences in circular orbits and the dynam- ics of light rings

    Vieira VF, Bernar RP, Macedo CF. Relativistic tidal divergences in circular orbits and the dynam- ics of light rings. arXiv preprint arXiv:2510.15705. 2025 Oct 17

    arXiv 2025

  47. [47]

    Particle motion and tidal force in a non-vacuum- charged naked singularity

    Viththani DP, Joshi AB, Bhanja T, Joshi PS. Particle motion and tidal force in a non-vacuum- charged naked singularity. The European Physical Journal C. 2024 Apr 10;84(4):383

    2024

  48. [48]

    Parametrized tidal dissipa- tion numbers of nonrotating black holes

    Kobayashi H, Mukohyama S, Oshita N, Takahashi K, Yingcharoenrat V. Parametrized tidal dissipa- tion numbers of nonrotating black holes. Physical Review D. 2025 Oct 15;112(8):084061.Goswami R, Ellis GF. Tidal forces are gravitational waves. Classical and Quantum Gravity. 2021 Apr 22;38(8):085023

    2025

  49. [49]

    Tidal forces are gravi- tational waves

    Goswami R, Ellis GF. Tidal forces are gravi- tational waves. Classical and Quantum Gravity. 2021 Apr 22;38(8):085023

    2021

  50. [50]

    Tidal force effects and periodic orbits in null naked singularity space- time

    Madan S, Bambhaniya P. Tidal force effects and periodic orbits in null naked singularity space- time. arXiv preprint arXiv:2201.13163. 2022 Jan 31

    Pith/arXiv arXiv 2022

  51. [51]

    Mechanisms behind the Aschenbach effect in non-rotating black hole spacetime

    Afshar MA, Sadeghi J. Mechanisms behind the Aschenbach effect in non-rotating black hole spacetime. Annals of Physics. 2025 Mar 1;474:169953

    2025

  52. [52]

    WGC as WCCC protector: The synergistic effects of various parameters in non-commutative black holes for identifying WGC candidate models

    Afshar MA, Sadeghi J. WGC as WCCC protector: The synergistic effects of various parameters in non-commutative black holes for identifying WGC candidate models. Nuclear Physics B. 2025 May 1;1014:116872

    2025

  53. [53]

    Kramer’s escape rate and phase transition dy- namics in AdS black holes

    Afshar MA, Noori Gashti S, Alipour MR, Sadeghi J. Kramer’s escape rate and phase transition dy- namics in AdS black holes. The European Physi- cal Journal C. 2025 Sep 3;85(9):939

    2025

  54. [54]

    Gashti, S.N., Afshar, M.A.S., Alipour, M.R. et al. Weak gravity conjecture in ModMax black holes: weak cosmic censorship and pho- ton sphere analysis. Eur. Phys. J. C 85, 1144 (2025). https://doi.org/10.1140/epjc/s10052-025- 14890-8 19

    doi:10.1140/epjc/s10052-025- 2025

  55. [55]

    Thermodynamic insights into ModMax-AdS black holes: A bridge between elec- trodynamic corrections and black hole physics

    Gashti SN, Afshar MA, Sekhmani Y, Shaymatov S, Jawad A, Alipour MR, Pourhassan B, Sadeghi J, Rayimbaev J. Thermodynamic insights into ModMax-AdS black holes: A bridge between elec- trodynamic corrections and black hole physics. Nuclear Physics B. 2025 Oct 3:117152

    2025

  56. [56]

    A deep dive into classical and topological CFT thermodynamics in lifshitz and hyperscaling vio- lating black holes

    Afshar MA, Alipour MR, Gashti SN, Sadeghi J. A deep dive into classical and topological CFT thermodynamics in lifshitz and hyperscaling vio- lating black holes. Fortschritte der Physik. 2025 Oct;73(9-10):e70030

    2025

  57. [57]

    Thermodynamic scalar curvature and topological classification in accelerating charged AdS black holes under rainbow gravity

    Gashti SN, Anand A, Singh A, Mishra A, Af- shar MA, Alipour MR, Sakallı İ, Pourhassan B, Sadeghi J. Thermodynamic scalar curvature and topological classification in accelerating charged AdS black holes under rainbow gravity. Physics of the Dark Universe. 2025 Oct 17:102136

    2025

  58. [58]

    Alipour, M.R., Gashti, S.N., Afshar, M.A.S. et al. Cooling and heating regions of Joule-Thomson expansion for AdS black holes: Einstein- Maxwell-power-Yang-Mills and Kerr Sen black holes. Gen Relativ Gravit 57, 61 (2025). https://doi.org/10.1007/s10714-025-03393-2

    work page doi:10.1007/s10714-025-03393-2 2025

  59. [59]

    Overcoming barriers: Kramers’ escape rate anal- ysis of metastable dynamics in first-order multi- phase transitions

    Afshar MA, Gashti SN, Alipour MR, Sadeghi J. Overcoming barriers: Kramers’ escape rate anal- ysis of metastable dynamics in first-order multi- phase transitions. Journal of High Energy Physics. 2025 Nov;2025(11):163

    2025

  60. [60]

    Weak gravity conjec- ture in ModMax black holes: weak cosmic censor- ship and photon sphere analysis

    Gashti SN, Afshar MA, Alipour MR, Sakallı İ, Pourhassan B, Sadeghi J. Weak gravity conjec- ture in ModMax black holes: weak cosmic censor- ship and photon sphere analysis. The European Physical Journal C. 2025 Oct;85(10):1-5

    2025

  61. [61]

    Thermodynamic signatures in black hole geometry and harmonic oscillations with non- linear electromagnetic fields and phantom global monopole

    Gashti SN, Sekhmani Y, Afshar MA, Alipour MR, Masouleh MK, Pourhassan B, Sadeghi J, Ray- imbaev J. Thermodynamic signatures in black hole geometry and harmonic oscillations with non- linear electromagnetic fields and phantom global monopole. Nuclear Physics B. 2025 Dec 4:117244

    2025

  62. [62]

    The Influence of Stable Photon Sphere Advent on Orbital Precession in moving towards the Extremality: Periapsis Shift as a Gateway to the Weak Gravity Conjecture

    Afshar MA, Sadeghi J. The Influence of Stable Photon Sphere Advent on Orbital Precession in moving towards the Extremality: Periapsis Shift as a Gateway to the Weak Gravity Conjecture. arXiv preprint arXiv:2511.07902. 2025 Nov 11

    Pith/arXiv arXiv 2025

  63. [63]

    Topological classification and black hole thermo- dynamics

    Alipour MR, Afshar MA, Gashti SN, Sadeghi J. Topological classification and black hole thermo- dynamics. Physics of the Dark Universe. 2023 Dec 1;42:101361

    2023

  64. [64]

    Topology of Hayward-AdS black hole thermodynamics

    Sadeghi J, Afshar MA, Noori Gashti S, Alipour MR. Topology of Hayward-AdS black hole thermodynamics. Physica Scripta. 2024 Feb 1;99(2):025003

    2024

  65. [65]

    Thermodynamic topology and photon spheres in the hyperscaling violating black holes

    Sadeghi J, Afshar MA, Gashti SN, Alipour MR. Thermodynamic topology and photon spheres in the hyperscaling violating black holes. Astropar- ticle Physics. 2024 Apr 1;156:102920

    2024

  66. [66]

    Bardeen black hole thermodynamics from topo- logical perspective

    Sadeghi J, Gashti SN, Alipour MR, Afshar MA. Bardeen black hole thermodynamics from topo- logical perspective. Annals of Physics. 2023 Aug 1;455:169391

    2023

  67. [67]

    Black holes with many horizons in the the- ories of nonlinear electrodynamics

    Gao C. Black holes with many horizons in the the- ories of nonlinear electrodynamics. Physical Re- view D. 2021 Sep 15;104(6):064038. 20

    2021