Journal of Physical Studies 27(4), Article 4901 [14 pages] (2023) DOI: https://doi.org/10.30970/jps.27.4901 DYNAMICS OF NEUTRAL AND CHARGED PARTICLE IN THE GRAVITATIONAL FIELD OF REISSNER–NORDSTRÖM BLACK HOLE IN THE PRESENCE OF EXTERNAL MAGNETIC FIELD AND DARK ENERGY Prosanta Mandal Department of Mathematics, Sripat Singh College, Jiaganj, Murshidabad, West Bengal, 742123, India, prosantamandal817@gmail.com Received 06 February 2023; in final form 24 August 2023; accepted 02 October 2023; published online 16 November 2023

I have studied the dynamics of a neutral and a charged particle around the Reissner-Nordström black hole surrounded by quintessence in the presence of an external magnetic field. The collision of a neutral particle moving around the black hole with another neutral particle has been discussed first. Then the collision of a charged particle moving around the black hole with another charged particle has been discussed. By numerical solution of the equations of motion it has been shown that after collision, if the particle gets sufficient energy, then it can escape to infinity. Dependence of orbits on the quintessence and the magnetic field for the charged particle has been studied in detail using the effective potential of the charged particle. Using the Lyapunov exponent effect of magnetic field and dark energy on the stability of the particle has been discussed. I have derived the expression for the center of mass energies of colliding charged particles moving around the black hole. Effective force on the charged particle due to dark energy and external magnetic field has been also discussed.

Key words: Euler–Lagrange equation, cyclic co-ordinate, escape velocity, center of mass energy and effective force.

Full text

1. V. P. Frolov, I. D. Novikov, Black Hole Physics, Basic Concepts and New Developments (Springer, 1998).
2. N. A. Sharp, Gen. Relativ. Gravit. 10, 659 (1979);
   Crossref
3. S. Perlmutter et al., Astrophys. J. 517, 565 (1999);
   Crossref
4. D. N. Spergel et al., Astrophys. J. Suppl. 170, 377 (2007);
   Crossref
5. M. Tegmark et al., Phys. Rev. D 69, 103501 (2004);
   Crossref
6. U. Seljak et al., Phys. Rev. D 71, 103515 (2005);
   Crossref
7. S. Weinberg, Rev. Mod. Phys. 61, 1 (1989);
   Crossref
8. P. J. E. Peebles, B. Ratra, Rev. Mod. Phys. 75, 559 (2003);
   Crossref
9. T. Padmanabhan, Phys. Rept. 380, 235 (2003);
   Crossref
10. L. Perivolaropoulos, preprint arXiv.0811.4684 (2008);
    Crossref
11. B. Ratra, P. J. E. Peebles, Phys. Rev. D 37, 3406 (1988);
    Crossref
12. J. M. Overduin, F. I. Cooperstock, Phys. Rev. D 58, 043506 (1998);
    Crossref
13. S. Basilakos, M. Plionis, J. Sola, Phys. Rev. D 80, 083511 (2009);
    Crossref
14. E. V. Linder, Phys. Rev. D 70, 023511 (2004);
    Crossref
15. J. A. S. Lima, F. E. Silva, R. C. Santos, Class. Quantum Gravity 25, 205006 (2008);
    Crossref
16. A. W. Brookfield, C. van de Bruck, D. F. Mota, D. T. Valentini, Phys. Rev. Lett. 96, 061301 (2006);
    Crossref
17. J. C. Mckinney, R. Narayan, Mon. Not. Roy. Astron. Soc. 375, 513 (2007);
    Crossref
18. C. V. Borm, M. Spaans, Astron. Astrophys. 553, L9 (2013);
    Crossref
19. V. Frolov, in The Galactic Black Hole: Lectures on General Relativity and Astrophysics, edited by H. Falcke and F. W. Hehl (Institute of Physics Publishing, Bristol–Philadelphia, 2003), p. 125.
20. P. B. Dobbie et al., in Proceedings of IAU Symposium 259 Galaxies (Tenerife, 2008), p. 129.
21. E. Teo, Gen. Relativ. Gravit. 35, 1909 (2003);
    Crossref
22. S. Hussain, I. Hussain, M. Jamil, Eur. Phys. J. C 74, 3210 (2014);
    Crossref
23. M. Jamil, S. Hussain, B. Majeed, Eur. Phys. J. C 75, 24 (2015);
    Crossref
24. S. Hussain, M. Jamil, Phys. Rev. D 92, 043008 (2015);
    Crossref
25. V. P. Frolov, A. A. Shoom, Phys. Rev. D 82, 084034 (2010);
    Crossref
26. B. Majeed, M. Jamil, S. Hussain, Adv. High Energy Phys. 2015, 671259 (2015);
    Crossref
27. V. V. Kiselev, Class. Quantum Gravity 20, 1187 (2003);
    Crossref
28. B. Malakolkalami, K. Ghaderi, Mod. Phys. Lett. 30 1550049 (2015);
    Crossref
29. S. Fernando, Gen. Relativ. Gravit. 44, 1857 (2012);
    Crossref
30. R. M. Wald, Phys. Rev. D 10, 1680 (1974);
    Crossref
31. A. N. Aliev, N. Ozdemir, Mon. Not. Roy. Astron. Soc. 336, 241 (2002);
    Crossref
32. A. M. Al Zahrani, V. P. Frolov, A. A. Shoom, Phys. Rev. D 87, 084043 (2013);
    Crossref
33. L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975).
34. M. Banados, J. Silk, S. M. West, Phys. Rev. Lett. 103, 111102 (2009);
    Crossref
35. V. Cardoso, A. S. Miranda, E. Berti, H. Witek, V. T. Zanchin, Phys. Rev. D 79 064016 (2009);
    Crossref
36. M. Visser, Class. Quant. Gravity 37, 045001 (2020);
    Crossref