Skip to main content
Log in

Distinguishable feature of electric and magnetic charged black hole

Acceleration of charged particle in Reissner–Nordström spacetime

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Obviously, from the geometrical point of view, it is impossible to distinguish the electrically and magnetically charged Reissner–Nordström black holes. One way of describing the differences between these solutions is to study the dynamical motion of charged test particles in the vicinity of the charged black hole and explore the effects of the charge coupling parameters (\(\sigma _e,\sigma _m\)) on the instability of the circular orbits. On the other hand, it is also possible to investigate the fundamental frequencies, such as Keplerian, Larmor, and epicyclic frequencies of charged particles orbiting around a charged black hole. Lastly, we investigate the synchrotron radiation by charged particles accelerated by charged black hole and estimate the intensity of relativistic radiating charged particles. Finally, we comment on the possible utilization of our findings for the relativistic jets and magneto-hydrodynamical outflows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Event Horizon Telescope Collaboration, First M87 event horizon telescope results: I-the shadow of the supermassive black hole. Astrophys. Lett. 875(1), L1 (2019). https://doi.org/10.3847/2041-8213/ab0ec7

  2. Event Horizon Telescope Collaboration, First M87 event horizon telescope results: II—array and instrumentation. Astrophys. Lett. 875(1), L2 (2019). https://doi.org/10.3847/2041-8213/ab0c96

  3. Event Horizon Telescope Collaboration, First M87 event horizon telescope results: III—data processing and calibration. Astrophys. Lett. 875(1), L3 (2019). https://doi.org/10.3847/2041-8213/ab0c57

  4. Event Horizon Telescope Collaboration, First M87 event horizon telescope results: IV—imaging the central supermassive black hole. Astrophys. Lett. 875(1), L4 (2019). https://doi.org/10.3847/2041-8213/ab0e85

  5. Event Horizon Telescope Collaboration, First M87 event horizon telescope results: V—physical origin of the asymmetric ring. Astrophys. Lett. 875(1), L5 (2019). https://doi.org/10.3847/2041-8213/ab0f43

  6. Event Horizon Telescope Collaboration, First M87 event horizon telescope results: VI—the shadow and mass of the central black hole. Astrophys. Lett. 875(1), L6 (2019). https://doi.org/10.3847/2041-8213/ab1141

  7. Gravity Collaboration, Detection of orbital motions near the last stable circular orbit of the massive black hole SgrA*. aap 618, L10 (2018). https://doi.org/10.1051/0004-6361/201834294

  8. G.D. Karssen, M. Bursa, A. Eckart, M. Valencia-S, M. Dovčiak, V. Karas, J. Horák, Bright X-ray flares from Sgr A*. mnras 472(4), 4422–4433 (2017). https://doi.org/10.1093/mnras/stx2312

    Article  ADS  Google Scholar 

  9. M. Zamaninasab, A. Eckart, M. Dovčiak, V. Karas, R. Schödel, G. Witzel, N. Sabha, M. García-Marín, D. Kunneriath, K. Mužić, C. Straubmeier, M. Valencia-S, J.A. Zensus, Near-infrared polarimetry as a tool for testing properties of accreting supermassive black holes. mnras 413(1), 322–332 (2011). https://doi.org/10.1111/j.1365-2966.2010.18139.x

    Article  ADS  Google Scholar 

  10. N. Dadhich, A. Tursunov, B. Ahmedov, Z. Stuchlík, The distinguishing signature of magnetic Penrose process. Mon. N. R. Astron. Soc. 478(1), L89–L94 (2018). https://doi.org/10.1093/mnrasl/sly073

    Article  ADS  Google Scholar 

  11. M. Kološ, A. Tursunov, Z. Stuchlík, Radiative Penrose process: Energy gain by a single radiating charged particle in the ergosphere of rotating black hole. Phys. Rev. D 103(2), 024021 (2021). https://doi.org/10.1103/PhysRevD.103.024021

    Article  ADS  MathSciNet  Google Scholar 

  12. Z. Stuchlík, M. Kološ, J. Kovář, P. Slaný, A. Tursunov, Influence of cosmic repulsion and magnetic fields on accretion disks rotating around Kerr Black Holes. Universe 6(2), 26 (2020). https://doi.org/10.3390/universe6020026

    Article  ADS  Google Scholar 

  13. A. Tursunov, Z. Stuchlík, M. Kološ, N. Dadhich, B. Ahmedov, Supermassive Black Holes as possible sources of ultrahigh-energy cosmic rays. Astrophys. J. 895(1), 14 (2020). https://doi.org/10.3847/1538-4357/ab8ae9

    Article  ADS  Google Scholar 

  14. A. Tursunov, M. Zajaček, A. Eckart, M. Kološ, S. Britzen, Z. Stuchlík, B. Czerny, V. Karas, Effect of electromagnetic interaction on galactic center flare components. Astrophys. J. 897(1), 99 (2020). https://doi.org/10.3847/1538-4357/ab980e

    Article  ADS  Google Scholar 

  15. S.M. Wagh, S.V. Dhurandhar, N. Dadhich, Revival of the penrose process for astrophysical applications. Astrphys. J 290, 12 (1985). https://doi.org/10.1086/162952

    Article  ADS  MathSciNet  Google Scholar 

  16. A. Tursunov, B. Juraev, Z. Stuchlík, M. Kološ, Electric Penrose process: high-energy acceleration of ionized particles by nonrotating weakly charged black hole. Phys. Rev. D 104(8), 084099 (2021). https://doi.org/10.1103/PhysRevD.104.084099

    Article  ADS  MathSciNet  Google Scholar 

  17. A.N. Chowdhury, M. Patil, D. Malafarina, P.S. Joshi, Circular geodesics and accretion disks in the Janis-Newman-Winicour and gamma metric spacetimes. Phys. Rev. D 85(10), 104031 (2012). https://doi.org/10.1103/PhysRevD.85.104031

    Article  ADS  Google Scholar 

  18. M. Patil, P.S. Joshi, Ultrahigh energy particle collisions in a regular spacetime without black holes or naked singularities. Phys. Rev. D 86(4), 044040 (2012). https://doi.org/10.1103/PhysRevD.86.044040

    Article  ADS  Google Scholar 

  19. Z. Stuchlík, J. Schee, Optical effects related to Keplerian discs orbiting Kehagias-Sfetsos naked singularities. Class. Quantum Gravity 31(19), 195013 (2014). https://doi.org/10.1088/0264-9381/31/19/195013

    Article  ADS  MATH  Google Scholar 

  20. Z. Stuchlík, J. Schee, A. Abdujabbarov, Ultra-high-energy collisions of particles in the field of near-extreme Kehagias-Sfetsos naked singularities and their appearance to distant observers. Phys. Rev. D 89(10), 104048 (2014). https://doi.org/10.1103/PhysRevD.89.104048

    Article  ADS  Google Scholar 

  21. C. Bambi, Probing the space-time geometry around black hole candidates with the resonance models for high-frequency QPOs and comparison with the continuum-fitting method. jcap 2012(9), 014 (2012). https://doi.org/10.1088/1475-7516/2012/09/014

    Article  Google Scholar 

  22. O. Dönmez, O. Zanotti, L. Rezzolla, On the development of quasi-periodic oscillations in Bondi-Hoyle accretion flows. mnras 412(3), 1659–1668 (2011). https://doi.org/10.1111/j.1365-2966.2010.18003.x

    Article  ADS  Google Scholar 

  23. P.J. Montero, O. Zanotti, Oscillations of relativistic axisymmetric tori and implications for modelling kHz-QPOs in neutron star X-ray binaries. mnras 419(2), 1507–1514 (2012). https://doi.org/10.1111/j.1365-2966.2011.19806.x

    Article  ADS  Google Scholar 

  24. Z. Stuchlík, A. Kotrlová, Orbital resonances in discs around braneworld Kerr black holes. Gen. Relativ. Gravit. 41, 1305–1343 (2009). https://doi.org/10.1007/s10714-008-0709-2

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. O. Zanotti, C. Roedig, L. Rezzolla, L. Del Zanna, General relativistic radiation hydrodynamics of accretion flows: I—Bondi-Hoyle accretion. mnras 417(4), 2899–2915 (2011). https://doi.org/10.1111/j.1365-2966.2011.19451.x

    Article  ADS  Google Scholar 

  26. M.A. Abramowicz, P.C. Fragile, Foundations of Black Hole Accretion Disk Theory. Living Rev. Relativ. 16(1), 1 (2013). https://doi.org/10.12942/lrr-2013-1

    Article  ADS  Google Scholar 

  27. D. Ghosh, A. Thalapillil, F. Ullah, Astrophysical hints for magnetic black holes. (2020). arXiv e-prints arXiv:2009.03363

  28. M. Zajaček, A. Tursunov, A. Eckart, S. Britzen, On the charge of the Galactic centre black hole. Mon. Not. R.A.S 480(4), 4408–4423 (2018). https://doi.org/10.1093/mnras/sty2182

    Article  ADS  Google Scholar 

  29. D. Pugliese, H. Quevedo, R. Ruffini, Circular motion of neutral test particles in Reissner-Nordström spacetime. Phys. Rev. D 83(2), 024021 (2011). https://doi.org/10.1103/PhysRevD.83.024021

    Article  ADS  Google Scholar 

  30. D. Bini, A. Geralico, R. Ruffini, On the equilibrium of a charged massive particle in the field of a Reissner Nordström black hole. Phys. Lett. A 360(4–5), 515–517 (2007). https://doi.org/10.1016/j.physleta.2006.09.028

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. P. Das, R. Sk, S. Ghosh, Motion of charged particle in Reissner-Nordström spacetime: a Jacobi-metric approach. Eur. Phys. J. C 77(11), 735 (2017). https://doi.org/10.1140/epjc/s10052-017-5295-6

    Article  ADS  Google Scholar 

  32. D. Pugliese, H. Quevedo, R. Ruffini, Motion of charged test particles in Reissner-Nordström spacetime. Phys. Rev. D 83(10), 104052 (2011). https://doi.org/10.1103/PhysRevD.83.104052

    Article  ADS  Google Scholar 

  33. D. Pugliese, H. Quevedo, R. Ruffini, General classification of charged test particle circular orbits in Reissner-Nordström spacetime. Eur. Phys. J. C 77(4), 206 (2017). https://doi.org/10.1140/epjc/s10052-017-4769-x

    Article  ADS  Google Scholar 

  34. B. Turimov, O. Rahimov, B. Ahmedov, Z. Stuchlík, K. Boymurodova, Dynamical motion of matter around a charged black hole. Int. J. Modern Phys. D 30(5), 2150037–407 (2021). https://doi.org/10.1142/S0218271821500371

    Article  ADS  MathSciNet  Google Scholar 

  35. S. Grunau, V. Kagramanova, Geodesics of electrically and magnetically charged test particles in the Reissner-Nordström space-time: analytical solutions. Phys. Rev. D 83(4), 044009 (2011). https://doi.org/10.1103/PhysRevD.83.044009

    Article  ADS  Google Scholar 

  36. A.F. Zakharov, Particle capture cross sections for a Reissner-Nordström black hole. Class. Quantum Gravity 11(4), 1027–1033 (1994). https://doi.org/10.1088/0264-9381/11/4/018

    Article  ADS  Google Scholar 

  37. B. Turimov, J. Rayimbaev, A. Abdujabbarov, B. Ahmedov, Z. Stuchlík, Test particle motion around a black hole in Einstein-Maxwell-scalar theory. Phys. Rev. D 102(6), 064052 (2020). https://doi.org/10.1103/PhysRevD.102.064052

    Article  ADS  MathSciNet  Google Scholar 

  38. M. Zhang, W.B. Liu, Innermost stable circular orbits of charged spinning test particles. Phys. Lett. B 789, 393–398 (2019). https://doi.org/10.1016/j.physletb.2018.12.051

    Article  ADS  MATH  Google Scholar 

  39. S. Hod, Quasinormal resonances of a charged scalar field in a charged Reissner-Nordström black-hole spacetime: a WKB analysis. Phys. Lett. B 710(2), 349–351 (2012). https://doi.org/10.1016/j.physletb.2012.03.010

    Article  ADS  MathSciNet  Google Scholar 

  40. S. Hod, Stability of the extremal Reissner-Nordström black hole to charged scalar perturbations. Phys. Lett. B 713(4–5), 505–508 (2012). https://doi.org/10.1016/j.physletb.2012.06.043

    Article  ADS  MathSciNet  Google Scholar 

  41. S. Hod, No-bomb theorem for charged Reissner-Nordström black holes. Phys. Lett. B 718(4–5), 1489–1492 (2013). https://doi.org/10.1016/j.physletb.2012.12.013

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. S. Hod, The instability spectrum of weakly-magnetized SU(2) Reissner-Nordström black holes. Phys. Lett. B 739, 157–161 (2014). https://doi.org/10.1016/j.physletb.2014.10.050

    Article  ADS  MathSciNet  Google Scholar 

  43. S. Hod, Numerical evidence for universality in the excited instability spectrum of magnetically charged Reissner-Nordström black holes. Eur. Phys. J. C 75, 180 (2015). https://doi.org/10.1140/epjc/s10052-015-3414-9

    Article  ADS  Google Scholar 

  44. S. Hod, Stability of highly-charged Reissner-Nordström black holes to charged scalar perturbations. Phys. Rev. D 91(4), 044047 (2015). https://doi.org/10.1103/PhysRevD.91.044047

    Article  ADS  MathSciNet  Google Scholar 

  45. O.B. Zaslavskii, Acceleration of particles by nonrotating charged black holes? Soviet J. Exp. Theor. Phys. Lett. 92(9), 571–574 (2010). https://doi.org/10.1134/S0021364010210010

    Article  Google Scholar 

  46. J. Rayimbaev, B. Turimov, F. Marcos, S. Palvanov, A. Rakhmatov, Particle acceleration and electromagnetic field of deformed neutron stars. Mod. Phys. Lett. A 35(9), 2050056 (2020). https://doi.org/10.1142/S021773232050056X

    Article  ADS  MathSciNet  Google Scholar 

  47. O. Zanotti, V. Morozova, B. Ahmedov, Particle acceleration in the polar cap region of an oscillating neutron star. Astron. Astrophys. 540, A126 (2012). https://doi.org/10.1051/0004-6361/201118380

    Article  ADS  Google Scholar 

  48. V. S. Morozova, B.J. Ahmedov, V.G. Kagramanova, General relativistic effects of gravitomagnetic charge on pulsar magnetospheres and particle acceleration in the polar cap. Astrophys. J 684(2), 1359–1365 (2008). https://doi.org/10.1086/590322

    Article  ADS  Google Scholar 

  49. A. Abdujabbarov, B. Ahmedov, Test particle motion around a black hole in a braneworld. Phys. Rev. D 81(4), 044022 (2010). https://doi.org/10.1103/PhysRevD.81.044022

    Article  ADS  Google Scholar 

  50. B. Turimov, Electromagnetic fields in vicinity of tidal charged static black hole. Int. J. Modern Phys. D 27, 1850092 (2018). https://doi.org/10.1142/S021827181850092X

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. H. Reissner, Über die eigengravitationn des elektrischen felds nach der Einsteinshen theorie. Ann. Phys. 50, 106–120 (1916)

    Article  Google Scholar 

  52. M. Tanabashi et al., Review of particle physics. Phys. Rev. D 98(3), 030,001 (2018). https://doi.org/10.1103/PhysRevD.98.030001

    Article  Google Scholar 

  53. P. Singh, N. Dadhich, Field theories from the relativistic law of motion. Mod. Phys. Lett. A 16(2), 83–90 (2001). https://doi.org/10.1142/S0217732301002900

    Article  ADS  MathSciNet  Google Scholar 

  54. P. Singh, N. Dadhich, The field equation from Newton’s law of motion and the absence of magnetic monopole. Int. J. Modern Phys. A 16(7), 1237–1247 (2001). https://doi.org/10.1142/S0217751X01003147

    Article  ADS  MathSciNet  MATH  Google Scholar 

  55. M. Kološ, Z. Stuchlík, A. Tursunov, Quasi-harmonic oscillatory motion of charged particles around a Schwarzschild black hole immersed in a uniform magnetic field. Class. Quantum Gravity 32(16), 165009 (2015). https://doi.org/10.1088/0264-9381/32/16/165009

    Article  ADS  MathSciNet  MATH  Google Scholar 

  56. B. Turimov, B. Ahmedov, M. Kološ, Z. Stuchlík, Axially symmetric and static solutions of Einstein equations with self-gravitating scalar field. Phys. Red. D 98(8), 084039 (2018). https://doi.org/10.1103/PhysRevD.98.084039

    Article  ADS  MathSciNet  Google Scholar 

  57. B. Turimov, B. Ahmedov, Z. Stuchlík, On exact analytical solution of Einstein-Maxwell-scalar field equations. Phys. Dark Univ. 33, 100868 (2021). https://doi.org/10.1016/j.dark.2021.100868

    Article  Google Scholar 

  58. A. Tursunov, Z. Stuchlík, M. Kološ, Circular orbits and related quasiharmonic oscillatory motion of charged particles around weakly magnetized rotating black holes. Phys. Rev. D 93(8), 084012 (2016). https://doi.org/10.1103/PhysRevD.93.084012

    Article  ADS  MathSciNet  Google Scholar 

  59. B. Turimov, B. Ahmedov, Zipoy-Voorhees gravitational object as a source of high-energy relativistic particles. Galaxies 9(3), 59 (2021). https://doi.org/10.3390/galaxies9030059

    Article  ADS  Google Scholar 

  60. M.A. Abramowicz, W. Kluźniak, A precise determination of black hole spin in GRO J1655-40. Astron. Astrophys. 374, L19–L20 (2001). https://doi.org/10.1051/0004-6361:20010791

    Article  ADS  Google Scholar 

  61. M.A. Abramowicz, W. Kluźniak, J.E. McClintock, R.A. Remillard, The importance of discovering a 3:2 twin-peak quasi-periodic oscillation in an ultraluminous X-Ray source, or how to solve the puzzle of intermediate-mass black holes. Astrophys. J. Lett. 609, L63–L65 (2004). https://doi.org/10.1086/422810

    Article  ADS  Google Scholar 

  62. A. Tursunov, M. Kološ, Z. Stuchlík, D.V. Gal’tsov, Radiation reaction of charged particles orbiting a magnetized Schwarzschild Black hole. Astrophys. J. 861(1), 2 (2018). https://doi.org/10.3847/1538-4357/aac7c5

    Article  ADS  Google Scholar 

  63. L.D. Landau, E.M. Lifshitz, The classical theory of fields, course of theoretical physics, vol. 2 (Elsevier Butterworth-Heinemann, Oxford, 2004)

    Google Scholar 

  64. V. S. Morozova, B. J. Ahmedov, V. G. Kagramanova, General relativistic effects of gravitomagnetic charge on pulsar magnetospheres and particle acceleration in the polar cap, Astrophys. J. 684(2), 1359–1365 (2008). https://doi.org/10.1086/590322

Download references

Acknowledgements

This research is supported by Grants F-FA-2021-432, F-FA-2021-510, and MRB-2021-527 of the Uzbekistan Ministry for Innovative Development and by the Abdus Salam International Centre for Theoretical Physics under the Grant No. OEA-NT-01. The authors thank Naresh Dadhich for useful discussions and comments on the black hole’s charge.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bobur Turimov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Turimov, B., Boboqambarova, M., Ahmedov, B. et al. Distinguishable feature of electric and magnetic charged black hole. Eur. Phys. J. Plus 137, 222 (2022). https://doi.org/10.1140/epjp/s13360-022-02390-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-02390-7

Navigation