On the light deflection and perihelion precession by BBMB black holes in HPM approximation

Authors

  • Victor Konstantinovich Shchigolev

    Department of Theoretical Physics, Ulyanovsk State University

How to Cite

Shchigolev, V. K. (2023). On the light deflection and perihelion precession by BBMB black holes in HPM approximation. International Journal of Scientific World, 9(1), 1-7. https://doi.org/10.14419/ijsw.v9i1.32342

Received date: September 6, 2023

Accepted date: September 6, 2023

Published date: September 19, 2023

DOI:

https://doi.org/10.14419/ijsw.v9i1.32342

Abstract

In this paper, the homotopy perturbation method (HPM) is applied for calculating the weak deflection angle and the perihelion precession angle of planetary orbits in the gravitational field of Bocharova-Bronnikov-Melnikov-Bekenstein (BBMB) black hole. Follow the procedure of HPM, we obtain the approximate solutions for the null and time-like geodesics in the gravitational field of BBMB black hole. On the basis of these solutions and the general formulae for the angle of deflection and the perihelion precession angle, derived by the author earlier via HPM, the corresponding angles for the BBMB black hole are obtained and compared with the similar angles in Schwarzschild spacetime. Notably that if the deflection angle obtained in this article using the HPM confirms the results of other researchers, then the perihelion precession angle obtained here for the first time can be compared with those known for a classical non-rotating static black hole.

References

  1. S. Weinberg, Gravitation and Cosmology: Principles and Applications of The General Theory of Relativity (John Wiley. Press, New York, 1972).
  2. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, W. H. Freeman and Co., San Francisco, Calif, USA, 1973.
  3. R. M. Wald, General Relativity, University of Chicago Press, Chicago, Ill, USA, 1984.
  4. G. V. Kraniotis, S. B. ”Whitehouse, Compact calculation of the Perihelion Precession of Mercury in General Relativity, the Cosmological Constant and
  5. Jacobi’s Inversion problem”, Class. Quant. Grav., Vol. 20, 4817-4835, 2003. DOI:10.1088/0264-9381/20/22/007
  6. Ya-Peng Hu, Hongsheng Zhang, Jun-Peng Hou, and Liang-Zun Tang, ”Perihelion Precession and Deflection of Light in the General Spherically
  7. Symmetric Spacetime”, Advances in High Energy Physics, Vol. 2014, Article ID 604321, 7 pages. http://dx.doi.org/10.1155/2014/604321
  8. W. Javed, M. B. Khadim, A. Ovg ¨ un, ”Weak gravitational lensing by Bocharova-Bronnikov-Melnikov-Bekenstein black holes using Gauss-Bonnet ¨
  9. theorem”, Eur. Phys. J. Plus, Vol. 135 , 595, 2020. https://doi.org/10.1140/epjp/s13360-020-00619-x
  10. M. V. Bebronne, P.G.Tinyakov, Erratum: ”Black hole solutions in massive gravity”, J. High Energ. Phys., Vol. 2011, 018, 2011.
  11. https://doi.org/10.1007/JHEP06(2011)018
  12. R. S. Kuniyal, R. Uniyal, A. Biswas, et al., ”Null geodesics and red-blue shifts of photons emitted from geodesic particles around a noncommutative
  13. black hole space-time”, Int. J. Modern Phys. A, Vol. 33, 1850098, 2018. https://doi.org/10.1142/S0217751X18500987
  14. M. K. Mak, C. S. Leung, and T. Harko, ”Computation of the General Relativistic Perihelion Precession and of Light Deflection via the Laplace-Adomian
  15. Decomposition Method”, Advances in High Energy Physics, Vol. 2018, Article ID 7093592, 15 pages. https://doi.org/10.1155/2018/7093592
  16. G. W. Gibbons and M. C. Werner, ”Classical and Quantum Gravity Applications of the Gauss-Bonnet theorem to gravitational lensing”, Class. Quantum
  17. Grav., Vol. 25, 235009, 2008. https://doi.org/10.1088/0264-9381/25/23/235009
  18. I. Sakalli, A. Ovg ¨ un, ”Hawking radiation and deflection of light from Rindler modified Schwarzschild black hole”, EPL, Vol. 118, 60006, 2017. ¨
  19. https://doi.org/10.1209/0295-5075/118/60006
  20. G. Crisnejo and E. Gallo, ”Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A
  21. unified treatment”, Phys. Rev. D 97, 124016 (2018). https://doi.org/10.1103/PhysRevD.97.124016
  22. J. Y. Kim, ”Deflection of light by a Coulomb charge in Born-Infeld electrodynamics”, Eur. Phys. J. C, Vol. 81, 508, 2021.
  23. https://doi.org/10.1140/epjc/s10052-021-09291-6
  24. S. W. Kim and Y. M. Cho, In: Evolution of the Universe and its Observational Quest (Universal Academy Press, Tokyo, 1994), p. 353.
  25. J. G. Cramer, R. L. Forward, M. S. Morris, et al., ”Natural wormholes as gravitational lenses”, Phys. Rev. D, Vol. 51, 3117, 1995.
  26. https://doi.org/10.1103/PhysRevD.51.3117
  27. K. Jusufi, N. Sarkar, F. Rahaman, et al., ”Deflection of light by black holes and massless wormholes in massive gravity”, Eur. Phys. J. C, Vol. 78, 349,
  28. https://doi.org/10.1140/epjc/s10052-018-5823-z
  29. J. Poutanen, ”Accurate analytic formula for light bending in Schwarzschild metric”, A&A Vol. 640, A24, 2020. https://doi.org/10.1051/0004-
  30. /202037471
  31. K. A. Bronnikov, K. A. Baleevskikh, ”On Gravitational Lensing by Symmetric and Asymmetric Wormholes”, Gravit. Cosmol., Vol. 25, 44-49, 2019.
  32. https://doi.org/10.1134/S020228931901002X
  33. C. Magnan, ”Complete calculations of the perihelion precession of Mercury and the deflection of light by the Sun in General Relativity”,
  34. http://arxiv.org/abs/0712.3709
  35. H. Arakida, ”Note on the Perihelion/Periastron Advance Due to Cosmological Constant”, Int. J. Theor. Phys., Vol. 52, 1408, 2013.
  36. https://doi.org/10.1007/s10773-012-1458-2
  37. L. S. Ridao, R. Avalos, M. D. De Cicco and M. Bellini, ”Perihelion advances for the orbits of Mercury, Earth and Pluto from Extended Theory of
  38. General Relativity (ETGR)”, https://doi.org/10.48550/arXiv.1402.4511
  39. A. A. Vankov, ”General Relativity Problem of Mercury’s Perihelion Advance Revisited”, http://arxiv.org/abs/1008.1811
  40. G. V. Kraniotis, S. B. Whitehouse, ”Compact calculation of the Perihelion Precession of Mercury in General Relativity, the Cosmological Constant and
  41. Jacobi’s Inversion problem”, Class. Quantum Grav., Vol. 20, 4817-4835, 2003. https://doi.org/10.1088/0264-9381/20/22/007
  42. T. Ono, T. Suzuki, N. Fushimi, K. Yamada, H. Asada, ”Marginally stable circular orbit of a test body in spherically symmetric and static spacetimes”,
  43. https://doi.org/10.48550/arXiv.1410.6265
  44. S.S. Ovcherenko, Z.K. Silagadze, ”Comment on perihelion advance due to cosmological constant”, Ukr. J. Phys., Vol. 61, 342-344, 2016.
  45. https://doi.org/10.15407/ujpe61.04.0342
  46. M. L. Ruggiero, ”Perturbations of Keplerian orbits in. stationary spherically symmetric spacetimes”, Int. J. Mod. Phys. D, Vol. 23, 1450049, 2014.
  47. https://doi.org/10.1142/S0218271814500497
  48. S. Chakraborty, S. SenGupta, ”Solar system constraints on alternative gravity theories”, Phys. Rev. D, Vol. 89, 026003, 2014.
  49. https://doi.org/10.1103/PhysRevD.89.026003
  50. R. R. Cuzinatto, P. J. Pompeia, M. de Montigny, et al., ”Classic tests of General Relativity described by brane-based spherically symmetric solutions”,
  51. Eur. Phys. J. C, Vol. 74, 3017, 2014. https://doi.org/10.1140/epjc/s10052-014-3017-x
  52. A. S. Fokas, C. G. Vayenas, D. Grigoriou, ”Analytical computation of the Mercury perihelion precession via the relativistic gravitational law and
  53. comparison with general relativity”, http://arxiv.org/abs/1509.03326
  54. Haotian Liu, Jinning Liang, Junji Jia, ”Deflection and Gravitational lensing of null and timelike signals in the Kiselev black hole spacetime in the weak
  55. field limit”, https://doi.org/10.48550/arXiv.2204.04519
  56. N. M. Bocharova, K. A. Bronnikov, and V. N. Melnikov, ”An exact solution of the system of Einstein equations and mass-free scalar field”, Vestn. Mosk.
  57. Univ. Ser. III Fiz. Astron., Vol. 6, 706, 1970.
  58. J. D. Bekenstein, ”Exact solutions of Einstein-conformal scalar equations”, Annals of Physics, Vol. 82(2), 535-547 (1974).
  59. J.-H. He, ”Homotopy perturbation technique”, Comput. Meth. Appl. Mech. Eng., Vol. 178, 257, 1999. https://doi.org/10.1016/S0045-7825(99)00018-3
  60. J.-H. He, ”A coupling method of a homotopy technique and a perturbation technique for non-linear problems”, Int. J. Nonlinear Mech., Vol. 35, 37,
  61. https://doi.org/10.1016/S0020-7462(98)00085-7
  62. L. Cveticanin, ”Homotopy-perturbation method for pure nonlinear differential equation”, Chaos Soliton Fract., Vol. 30, 1221, 2006.
  63. https://doi.org/10.1016/j.chaos.2005.08.180
  64. M. Zare, O. Jalili and M. Delshadmanesh, ”Two binary stars gravitational waves: homotopy perturbation method”, Indian J. Phys., Vol. 86, 855, 2012.
  65. https://doi.org/10.1007/s12648-012-0154-7
  66. V. Shchigolev, ”Homotopy Perturbation Method for Solving a Spatially Flat FRW Cosmological Model”, Univ. J. Applied Math., Vol. 2, 99, 2014. DOI:
  67. 13189/ujam.2014.020204
  68. V. Shchigolev, ”Analytical Computation of the Perihelion Precession in General Relativity via the Homotopy Perturbation Method”, Univ. J. Comput.
  69. Math., Vol. 3, 45, 2015. DOI: 10.13189/ujcmj.2015.030401
  70. F. Rahaman, S. Ray, A. Aziz, S. R. Chowdhury, D. Deb, ”Exact Radiation Model For Perfect Fluid Under Maximum Entropy Principle”,
  71. https://doi.org/10.48550/arXiv.1504.05838
  72. V. K. Shchigolev, ”Calculating luminosity distance versus redshift in FLRW cosmology via homotopy perturbation method”, Gravit.Cosmol., Vol. 23,
  73. -148, 2017. https://doi.org/10.1134/S0202289317020098
  74. V. K. Shchigolev, D. N. Bezbatko, ”On HPM approximation for the perihelion precession angle in general relativity”, Int. J. Adv. Astron., Vol. 5(1), 38,
  75. doi:10.14419/ijaa.v5i1.7279
  76. V. K. Shchigolev, D. N. Bezbatko, ”Studying Gravitational Deflection of Light by Kiselev Black Hole via Homotopy Perturbation Method”, Gen. Rel.
  77. Grav., Vol. 51, 34, 2019. ttps://doi.org/10.1007/s10714-019-2521-6
  78. V. K. Shchigolev, ”Exact solutions to the null-geodesics in Ellis-Bronnikov wormhole spacetime via (G’/G)-expansion method”, Modern Physics Letters
  79. A, Vol. 37, No. 20, 2250124, 2022. https://doi.org/10.1142/S0217732322501243
  80. V. K. Shchigolev, ”Exact analytical solutions to the geodesic equations in general relativity via (G’/G) - expansion method”, Gen Relativ Gravit, Vol. 54,
  81. 2022. https://doi.org/10.1007/s10714-022-02964-x

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How to Cite

Shchigolev, V. K. (2023). On the light deflection and perihelion precession by BBMB black holes in HPM approximation. International Journal of Scientific World, 9(1), 1-7. https://doi.org/10.14419/ijsw.v9i1.32342

Received date: September 6, 2023

Accepted date: September 6, 2023

Published date: September 19, 2023