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Charged Binaries in Gravitational Tides

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Pith's one-line read Tidal corrections to the ISCO and light ring of a Reissner-Nordström black hole are derived analytically and shown to be suppressed but non-vanishing at extremality.

arxiv 2411.08089 v1 pith:3JCA4YET submitted 2024-11-12 gr-qc astro-ph.HEhep-th

Elisa Grilli , Marta Orselli , David Pereñiguez , Daniele Pica This is my paper · ORCID
classification gr-qcastro-ph.HEhep-th
keywords binaryblackgravitationaltidalchargedholesystemseffects
verification ladder T0 review T1 audit T2 compute T3 formal

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The reading

This paper studies a small black hole (or test particle) orbiting a larger charged black hole, while an even more distant supermassive black hole pulls on the pair with its gravity. This setup is called a hierarchical triple. The authors want to know how the external tide changes the location of the innermost stable circular orbit (ISCO) and the light ring, the two special radii that control where matter and light can orbit stably.

They first construct the deformation of a charged (Reissner-Nordström) black hole caused by a stationary external tide, using linearized Einstein-Maxwell theory. Then they compute the averaged, or secular, Hamiltonian of a test particle on a nearly circular orbit. From that Hamiltonian they derive explicit formulas for how the ISCO and light ring radii, energy, angular momentum, and orbital frequency shift, as functions of the black hole's mass and charge.

The main physical finding is that the tidal shifts become smaller as the black hole's charge-to-mass ratio increases, because the charged black hole's gravitational well is shallower and its 'throat' is longer, dragging these special orbits inward. However, even in the extreme limit where the charge equals the mass, the shifts do not vanish; they converge to finite, calculable values. If the test particle is itself charged, there is an additional electromagnetic contribution, but the gravitational effect dominates for the cases considered.

The calculation is purely analytic. No numerical simulations or observations are presented. The authors suggest the method can be extended to other compact objects, such as topological stars, and that the results may anticipate the behavior of rotating black holes.

Extended reading notes

Core claim

The tidal corrections to the ISCO and light ring parameters of a charged black hole are monotonically decreasing functions of the charge-to-mass ratio Q/M and converge to a finite, non-zero value in the extremal limit (eqs. (4.7), (4.13), (4.9), (4.14)). If correct, the leading-order effect of an external tide on a charged EMRI is fully captured by these analytic formulas.

Load-bearing premise

The secular Hamiltonian (3.4) is obtained by averaging over the test particle's azimuthal angle (3.3), which retains only the m=0 component of the tidal field. The paper does not explicitly justify that non-axisymmetric (m≠0) components of a general quadrupolar tide produce no first-order secular correction to the ISCO and light ring. This assumption enters at eqs. (3.3)-(3.5) and is the bridge between the physical tide and the computed shifts.

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

The central claim rests on the perturbation formalism of [47], physical boundary conditions, and the secular averaging assumption; no free parameters are fitted to data. The results are analytic functions of M, Q, and the tidal amplitude.

assumptions (5)
  • domain assumption The linearized Einstein-Maxwell perturbation decomposition (2.7)-(2.8) from [47] is valid and complete for stationary tides on dyonic RN.
    The paper does not derive the perturbation equations; it cites [47] and presents the solution. This is the foundation for the tidal background.
  • domain assumption Boundary conditions at infinity: electromagnetic master variables grow as r^ℓ, selecting a purely gravitational tide.
    Sec. 2.2; this excludes electromagnetic tidal sources, a physical restriction that determines the unique solution.
  • domain assumption Secular averaging over ϕ retains only the m=0 tide component; m≠0 components give no first-order secular effect.
    Used in (3.5) to obtain the averaged Hamiltonian (3.4). Not explicitly justified in the text.
  • domain assumption Test particle approximation: m/M small and M/R small, with R the tidal length scale.
    Sec. 3; justifies neglecting self-force and higher multipoles.
  • domain assumption Expansion in q̃ ≪ 1 for charged particles is valid, excluding elementary particles.
    Sec. 4.2; this restricts the regime of validity of the charged-particle results.

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Pith. "Pith review of Charged Binaries in Gravitational Tides." pith.science (2026). https://pith.science/paper/3JCA4YET

@misc{pith2026241108089,
  author       = {Pith},
  title        = {Pith review of: Charged Binaries in Gravitational Tides},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3JCA4YET}},
  note         = {Machine review of arXiv:2411.08089}
}
read the original abstract

Next-generation low-frequency interferometers are expected to detect binary systems near supermassive black holes, where tidal effects can alter significantly the motion of the binary. This motivates a broader investigation of how external gravitational fields influence the dynamics of physical systems. In this work, we consider a charged black hole binary system subject to a gravitational tide. We first construct a stationary gravitational tide acting on a dyonic Reissner-Nordstr\"om black hole and, focusing on the extreme mass-ratio limit, we analyze the motion of a test particle. By calculating the secular Hamiltonian of the test particle, we obtain the ISCO and light ring tidal shifts in terms of explicit functions of the parameters of the binary. Our results show that tidal corrections are suppressed as the charge of the black hole increases, but they persist in the extremal limit yielding a finite contribution. This work paves the way towards studying tidal effects on other charged systems, such as topological stars.

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

  1. Tidal perturbations of an extreme mass ratio inspiral around a Kerr black hole

    gr-qc 2026-01 conditional novelty 6.0 of 10

    A closed-form Kerr metric under slow quadrupolar tides yields spin-dependent tidal shifts of the ISCO and light ring, with larger shifts for retrograde orbits around fast-spinning holes.

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Works this paper leans on

68 extracted references · 26 canonical work pages · cited by 1 Pith paper

  1. [1]

    E. E. Flanagan and T. Hinderer, Constraining neutron star tidal Love numbers with gravitational wave detectors , Phys. Rev. D 77 (2008) 021502 [ 0709.1915]

    arXiv 2008

  2. [2]

    Hinderer, Tidal Love numbers of neutron stars , Astrophys

    T. Hinderer, Tidal Love numbers of neutron stars , Astrophys. J. 677 (2008) 1216–1220 [0711.2420]. [Erratum: Astrophys.J. 697, 964 (2009)]

    arXiv 2008

  3. [3]

    Hinderer, B

    T. Hinderer, B. D. Lackey, R. N. Lang and J. S. Read, Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral , Phys. Rev. D 81 (2010) 123016 [ 0911.3535]

    arXiv 2010

  4. [4]

    Cardoso and F

    V. Cardoso and F. Duque, Environmental effects in gravitational-wave physics: Tidal deformability of black holes immersed in matter , Phys. Rev. D 101 (2020), no. 6 064028 [1912.07616]

    arXiv 2020

  5. [5]

    Katagiri, V

    T. Katagiri, V. Cardoso, T. Ikeda and K. Yagi, Tidal response beyond vacuum General Relativity with a canonical definition , 2410.02531

    arXiv

  6. [6]

    Binnington and E

    T. Binnington and E. Poisson, Relativistic theory of tidal Love numbers , Phys. Rev. D 80 (2009) 084018 [ 0906.1366]

    arXiv 2009

  7. [7]

    Zhang and X

    Z. Zhang and X. Chen, The Dynamics and Gravitational-wave Signal of a Binary Flying Closely by a Kerr Supermassive Black Hole , Astrophys. J. 968 (2024), no. 2 122 [ 2402.02178]

    arXiv 2024

  8. [8]

    Chen and W.-B

    X. Chen and W.-B. Han, A New Type of Extreme-mass-ratio Inspirals Produced by Tidal Capture of Binary Black Holes , Communications Physics 1 (2018) 53 [ 1801.05780]. – 19 –

    arXiv 2018

Show all 68 references
  1. [9]

    Addison, M

    E. Addison, M. Gracia-Linares, P. Laguna and S. L. Larson, Busting up binaries: encounters between compact binaries and a supermassive black hole , General Relativity and Gravitation 51 (2019), no. 3 38

    2019

  2. [10]

    Chen and Z

    X. Chen and Z. Zhang, Binaries wandering around supermassive black holes due to gravitoelectromagnetism, Phys. Rev. D 106 (Nov, 2022) 103040

    2022

  3. [11]

    Amaro-Seoane, Relativistic dynamics and extreme mass ratio inspirals , Living Reviews in Relativity 21 (May, 2018)

    P. Amaro-Seoane, Relativistic dynamics and extreme mass ratio inspirals , Living Reviews in Relativity 21 (May, 2018)

    2018

  4. [12]

    Amaro Seoane, The Gravitational Capture of Compact Objects by Massive Black Holes , p

    P. Amaro Seoane, The Gravitational Capture of Compact Objects by Massive Black Holes , p. 1–79. Springer Singapore, 2021

    2021

  5. [13]

    Amaro-Seoane, J

    P. Amaro-Seoane, J. R. Gair, M. Freitag, M. C. Miller, I. Mandel, C. J. Cutler and S. Babak, Intermediate and extreme mass-ratio inspirals—astrophysics, science applications and detection using lisa , Classical and Quantum Gravity 24 (Aug., 2007) R113–R169

    2007

  6. [14]

    C. P. L. Berry, S. A. Hughes, C. F. Sopuerta, A. J. K. Chua, A. Heffernan, K. Holley-Bockelmann, D. P. Mihaylov, M. C. Miller and A. Sesana, The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy , 2019

    2019

  7. [15]

    Peng and X

    P. Peng and X. Chen, The last migration trap of compact objects in AGN accretion disc , Mon. Not. Roy. Astron. Soc. 505 (2021), no. 1 1324–1333 [ 2104.07685]

    2021 arXiv

  8. [16]

    J. M. Bellovary, M.-M. M. Low, B. McKernan and K. E. S. Ford, Migration traps in disks around supermassive black holes , The Astrophysical Journal Letters 819 (Mar., 2016) L17

    2016

  9. [17]

    Secunda, B

    A. Secunda, B. Hernandez, J. Goodman, N. W. C. Leigh, B. McKernan, K. E. S. Ford and J. I. Adorno, Evolution of retrograde orbiters in an active galactic nucleus disk , The Astrophysical Journal Letters 908 (Feb., 2021) L27

    2021

  10. [18]

    Yang and M

    H. Yang and M. Casals, General Relativistic Dynamics of an Extreme Mass-Ratio Binary interacting with an External Body , Phys. Rev. D 96 (2017), no. 8 083015 [ 1704.02022]

    2017 arXiv

  11. [19]

    Camilloni, G

    F. Camilloni, G. Grignani, T. Harmark, R. Oliveri, M. Orselli and D. Pica, Tidal deformations of a binary system induced by an external Kerr black hole , Phys. Rev. D 107 (2023), no. 8 084011 [2301.04879]

    2023 arXiv

  12. [20]

    Cardoso and A

    V. Cardoso and A. Foschi, Geodesic structure and quasinormal modes of a tidally perturbed spacetime, Physical Review D 104 (July, 2021)

    2021

  13. [21]

    Camilloni, T

    F. Camilloni, T. Harmark, G. Grignani, M. Orselli and D. Pica, Binary mergers in strong gravity background of Kerr black hole , Mon. Not. Roy. Astron. Soc. 531 (2024), no. 1 1884–1904 [2310.06894]

    2024 arXiv

  14. [22]

    F. J. Zerilli, Perturbation analysis for gravitational and electromagnetic radiation in a reissner-nordstroem geometry, Phys. Rev. D 9 (1974) 860–868

    1974

  15. [23]

    Johnston, R

    M. Johnston, R. Ruffini and F. Zerilli, Electromagnetically induced gravitational radiation, Phys. Lett. B 49 (1974) 185–188

    1974

  16. [24]

    Moncrief, Stability of reissner-nordstr¨ om black holes, Phys

    V. Moncrief, Stability of reissner-nordstr¨ om black holes, Phys. Rev. D 10 (Aug, 1974) 1057–1059

    1974

  17. [25]

    U. H. Gerlach and U. K. Sengupta, GAUGE INV ARIANT PERTURBATIONS ON MOST GENERAL SPHERICALLY SYMMETRIC SPACE-TIMES , Phys. Rev. D 19 (1979) 2268–2272

    1979

  18. [26]

    U. H. Gerlach and U. K. Sengupta, GAUGE INV ARIANT COUPLED GRA VITATIONAL, ACOUSTICAL, AND ELECTROMAGNETIC MODES ON MOST GENERAL SPHERICAL SPACE-TIMES, Phys. Rev. D 22 (1980) 1300–1312. – 20 –

    1980

  19. [27]

    Chandrasekhar and B

    S. Chandrasekhar and B. C. Xanthopoulos, On the metric perturbations of the reissner–nordstr¨ om black hole, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 367 (1979) 1 – 14

    1979

  20. [28]

    R. M. Wald, Black hole in a uniform magnetic field , Phys. Rev. D 10 (1974) 1680–1685

    1974

  21. [29]

    Kritos and J

    K. Kritos and J. Silk, Mergers of maximally charged primordial black holes , Phys. Rev. D 105 (2022), no. 6 063011 [ 2109.09769]

    2022 arXiv

  22. [30]

    De Rujula, S

    A. De Rujula, S. L. Glashow and U. Sarid, CHARGED DARK MATTER, Nucl. Phys. B333 (1990) 173

    1990

  23. [31]

    M. L. Perl and E. R. Lee, The search for elementary particles with fractional electric charge and the philosophy of speculative experiments , Am. J. Phys. 65 (1997) 698–706

    1997

  24. [32]

    Holdom, Two U(1)’s and Epsilon Charge Shifts , Phys

    B. Holdom, Two U(1)’s and Epsilon Charge Shifts , Phys. Lett. B166 (1986) 196

    1986

  25. [33]

    Sigurdson, M

    K. Sigurdson, M. Doran, A. Kurylov, R. R. Caldwell and M. Kamionkowski, Dark-matter electric and magnetic dipole moments , Phys. Rev. D70 (2004) 083501 [ astro-ph/0406355]. [Erratum: Phys. Rev.D73,089903(2006)]

    2004 arXiv

  26. [34]

    Davidson, S

    S. Davidson, S. Hannestad and G. Raffelt, Updated bounds on millicharged particles , JHEP 05 (2000) 003 [ hep-ph/0001179]

    2000 arXiv

  27. [35]

    S. D. McDermott, H.-B. Yu and K. M. Zurek, Turning off the Lights: How Dark is Dark Matter?, Phys. Rev. D 83 (2011) 063509 [ 1011.2907]

    2011 arXiv

  28. [36]

    Cardoso, C

    V. Cardoso, C. F. B. Macedo, P. Pani and V. Ferrari, Black holes and gravitational waves in models of minicharged dark matter , JCAP 05 (2016) 054 [ 1604.07845]. [Erratum: JCAP 04, E01 (2020)]

    2016 arXiv

  29. [37]

    Khalil, N

    M. Khalil, N. Sennett, J. Steinhoff, J. Vines and A. Buonanno, Hairy binary black holes in Einstein-Maxwell-dilaton theory and their effective-one-body description , Phys. Rev. D 98 (2018), no. 10 104010 [ 1809.03109]

    2018 arXiv

  30. [38]

    Bai and N

    Y. Bai and N. Orlofsky, Primordial Extremal Black Holes as Dark Matter , Phys. Rev. D 101 (2020), no. 5 055006 [ 1906.04858]

    2020 arXiv

  31. [39]

    P. K. Gupta, T. F. M. Spieksma, P. T. H. Pang, G. Koekoek and C. V. D. Broeck, Bounding dark charges on binary black holes using gravitational waves , Phys. Rev. D 104 (2021), no. 6 063041 [2107.12111]

    2021 arXiv

  32. [40]

    A. M. Polyakov, Particle Spectrum in Quantum Field Theory , JETP Lett. 20 (1974) 194–195

    1974

  33. [41]

    ’t Hooft, Magnetic Monopoles in Unified Gauge Theories , Nucl

    G. ’t Hooft, Magnetic Monopoles in Unified Gauge Theories , Nucl. Phys. B 79 (1974) 276–284

    1974

  34. [42]

    Maldacena, Comments on magnetic black holes , JHEP 04 (2021) 079 [ 2004.06084]

    J. Maldacena, Comments on magnetic black holes , JHEP 04 (2021) 079 [ 2004.06084]

    2021 arXiv

  35. [43]

    G. W. Gibbons, Black Hole Dyons Need Not Explode , Phys. Rev. D 15 (1977) 3530

    1977

  36. [44]

    L. Liu, O. Christiansen, Z.-K. Guo, R.-G. Cai and S. P. Kim, Gravitational and electromagnetic radiation from binary black holes with electric and magnetic charges: Circular orbits on a cone , Phys. Rev. D 102 (2020), no. 10 103520 [ 2008.02326]

    2020 arXiv

  37. [45]

    L. Liu, O. Christiansen, W.-H. Ruan, Z.-K. Guo, R.-G. Cai and S. P. Kim, Gravitational and electromagnetic radiation from binary black holes with electric and magnetic charges: elliptical orbits on a cone , Eur. Phys. J. C 81 (2021), no. 11 1048 [ 2011.13586]

    2021 arXiv

  38. [46]

    Z.-C. Chen, S. P. Kim and L. Liu, Gravitational and electromagnetic radiation from binary black holes with electric and magnetic charges: hyperbolic orbits on a cone , Commun. Theor. Phys. 75 (2023), no. 6 065401 [ 2210.15564]

    2023 arXiv

  39. [47]

    Pere˜ niguez,Black hole perturbations and electric-magnetic duality , Phys

    D. Pere˜ niguez,Black hole perturbations and electric-magnetic duality , Phys. Rev. D 108 (2023), no. 8 084046 [ 2302.10942]. – 21 –

    2023 arXiv

  40. [48]

    Pere˜ niguez, M

    D. Pere˜ niguez, M. de Amicis, R. Brito and R. Panosso Macedo, Superradiant Instability of Magnetic Black Holes , 2402.05178

    arXiv

  41. [49]

    Gervalle and M

    R. Gervalle and M. S. Volkov, Black Holes with Electroweak Hair , Phys. Rev. Lett. 133 (2024), no. 17 171402 [ 2406.14357]

    2024 arXiv

  42. [50]

    P. V. P. Cunha, C. A. R. Herdeiro, E. Radu and N. M. Santos, Breaking the north-south symmetry: dyonic spinning black holes with synchronized gauged scalar hair , 2410.21421

    arXiv

  43. [51]

    Dyson and D

    C. Dyson and D. Pere˜ niguez,Magnetic black holes: From Thomson dipoles to the Penrose process and cosmic censorship, Phys. Rev. D 108 (2023), no. 8 084064 [ 2306.15751]

    2023 arXiv

  44. [52]

    De Felice and S

    A. De Felice and S. Tsujikawa, Probing the signature of axions through the quasinormal modes of black holes , Phys. Lett. B 855 (2024) 138808 [ 2402.08868]

    2024 arXiv

  45. [53]

    Bah and P

    I. Bah and P. Heidmann, Topological Stars and Black Holes , Phys. Rev. Lett. 126 (2021), no. 15 151101 [ 2011.08851]

    2021 arXiv

  46. [54]

    A. Dima, M. Melis and P. Pani, Spectroscopy of magnetized black holes and topological stars , 2406.19327

    arXiv

  47. [55]

    I. Bena, G. Di Russo, J. F. Morales and A. Ruip´ erez,Non-spinning tops are stable , 2406.19330

    arXiv

  48. [56]

    Poisson and I

    E. Poisson and I. Vlasov, Geometry and dynamics of a tidally deformed black hole , Phys. Rev. D 81 (2010) 024029 [ 0910.4311]

    2010 arXiv

  49. [57]

    Cardoso, E

    V. Cardoso, E. Franzin, A. Maselli, P. Pani and G. Raposo, Testing strong-field gravity with tidal Love numbers , Phys. Rev. D 95 (2017), no. 8 084014 [ 1701.01116]. [Addendum: Phys.Rev.D 95, 089901 (2017)]

    2017 arXiv

  50. [58]

    Poisson, Tidally induced multipole moments of a nonrotating black hole vanish to all post-Newtonian orders, Phys

    E. Poisson, Tidally induced multipole moments of a nonrotating black hole vanish to all post-Newtonian orders, Phys. Rev. D 104 (2021), no. 10 104062 [ 2108.07328]

    2021 arXiv

  51. [59]

    Rai and L

    M. Rai and L. Santoni, Ladder symmetries and Love numbers of Reissner-Nordstr¨ om black holes, JHEP 07 (2024) 098 [ 2404.06544]

    2024 arXiv

  52. [60]

    Pere˜ niguez and V

    D. Pere˜ niguez and V. Cardoso,Love numbers and magnetic susceptibility of charged black holes, Phys. Rev. D 105 (2022), no. 4 044026 [ 2112.08400]

    2022 arXiv

  53. [61]

    Charalambous, Love numbers and Love symmetries for p-form and gravitational perturbations of higher-dimensional spherically symmetric black holes , JHEP 04 (2024) 122 [2402.07574]

    P. Charalambous, Love numbers and Love symmetries for p-form and gravitational perturbations of higher-dimensional spherically symmetric black holes , JHEP 04 (2024) 122 [2402.07574]

    2024 arXiv

  54. [62]

    Isoyama, L

    S. Isoyama, L. Barack, S. R. Dolan, A. Le Tiec, H. Nakano, A. G. Shah, T. Tanaka and N. Warburton, Gravitational self-force correction to the innermost stable circular equatorial orbit of a kerr black hole , Phys. Rev. Lett. 113 (Oct, 2014) 161101

    2014

  55. [63]

    S. L. Detweiler, A Consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry, Phys. Rev. D 77 (2008) 124026 [ 0804.3529]

    2008 arXiv

  56. [64]

    Pugliese and R

    D. Pugliese and R. Ruffini, Circular motion of neutral test particles in reissner-nordstr¨ om spacetime, Phys. Rev. D 83 (01, 2011)

    2011

  57. [65]

    Pugliese, H

    D. Pugliese, H. Quevedo and R. Ruffini, Circular motion in Reissner-Nordstr¨ om spacetime, 1003.2687

    arXiv

  58. [66]

    Pugliese, H

    D. Pugliese, H. Quevedo and R. Ruffini, Equatorial circular orbits of neutral test particles in the Kerr-Newman spacetime , Phys. Rev. D 88 (2013), no. 2 024042 [ 1303.6250]

    2013 arXiv

  59. [67]

    P. Das, R. Sk and S. Ghosh, Motion of charged particle in Reissner–Nordstr¨ om spacetime: a Jacobi-metric approach, Eur. Phys. J. C 77 (2017), no. 11 735 [ 1609.04577]

    2017 arXiv

  60. [68]

    Tsukamoto, Gravitational lensing by a photon sphere in a Reissner-Nordstr¨ om naked singularity spacetime in strong deflection limits , Phys

    N. Tsukamoto, Gravitational lensing by a photon sphere in a Reissner-Nordstr¨ om naked singularity spacetime in strong deflection limits , Phys. Rev. D 104 (2021), no. 12 124016 [2107.07146]. – 22 –

    2021 arXiv

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