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Influence of a Cosmic String on the Rate of Pairs Produced by the Coulomb Potential

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Abstract

We study particle creation phenomenon by the Coulomb potential of an external electric field in the presence of a gravitational field of a static cosmic string. For that, the generalized Klein-Gordon and Dirac equations are solved, and by using the Bogoliubov transformation we calculate the probability and the number density of created particles. It is shown that the presence of the cosmic string enhances the particle production. For the grand unified theory (GUT) cosmic string, the production of spinless particles is possible if the Coulomb potential nucleus charge \(Z\ge 206\), and for spin-1/2 particles if \(Z\ge 275\).

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References

  1. Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982)

    Book  MATH  Google Scholar 

  2. Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975). https://doi.org/10.1007/BF02345020

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Bernard, C., Duncan, A.: Regularization and renormalization of quantum field theory in curved space-time. Ann. Phys. 107, 201 (1977). https://doi.org/10.1016/0003-4916(77)90210-X

    Article  ADS  MATH  Google Scholar 

  4. Lapedes, A.S.: Euclidean quantum field theory and the Hawking effect. Phys. Rev. D 17, 2556 (1978). https://doi.org/10.1103/PhysRevD.17.2556

    Article  ADS  Google Scholar 

  5. Buchbinder, I.L., Odintsov, S.D.: Creation of particles and the effective lagrangian in the quasieuclidean model of the universe with an electromagnetic field. Sov. Phys. J. 25, 385 (1982). https://doi.org/10.1007/BF00891754

    Article  Google Scholar 

  6. Mottola, E.: Particle creation in de Sitter space. Phys. Rev. D 31, 754 (1985). https://doi.org/10.1103/Phys-RevD.31.754

  7. Lotze, K.H.: Production of massive spin-1/2 particles in Robertson-Walker universes with external electromagnetic fields. Astrophys. Space Sci. 120, 191 (1986). https://doi.org/10.1007/BF00649935

    Article  ADS  MathSciNet  Google Scholar 

  8. Garriga, J.: Pair production by an electric field in (1+1)-dimensional de Sitter space. Phys. Rev. D 49, 6343 (1994). https://doi.org/10.1103/PhysRevD.49.6343

    Article  ADS  Google Scholar 

  9. Gavrilov, S.P., Gitman, D.M., Odintsov, S.D.: Quantum scalar field in FRW universe with constant electromagnetic background. Int. J. Mod. Phys. A 12, 4837 (1997). https://doi.org/10.1142/S0217751X97002589

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Villalba, V., Greiner, W.: Creation of Dirac particles in the presence of a constant electric field in an anisotropic Bianchi I universe. Mod. Phys. Lett. A 17, 1883 (2002). https://doi.org/10.1142/S0217732302008289

    Article  ADS  MATH  Google Scholar 

  11. Mendy, J.E.B.: Scalar and spin-1/2 particle creation in gravitational and constant electric field backgrounds. J. Math. Phys. 44, 662 (2003). https://doi.org/10.1063/1.1500793

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Falek, M., Merad, M.: Duffin-Kemmer-Petiau equation in Robertson-Walker space-time. Open Physics 8, 408 (2010). https://doi.org/10.2478/s11534-009-0112-y

    Article  ADS  MATH  Google Scholar 

  13. Haouat, S., Chekireb, R.: Schwinger effect in a Robertson-Walker space-time. Int. J. Theo. Phys. 51, 1704 (2012). https://doi.org/10.1007/s10773-011-1048-8

    Article  MathSciNet  MATH  Google Scholar 

  14. Haouat, S., Chekireb, R.: Effect of electromagnetic fields on the creation of scalar particles in a flat Robertson-Walker space-time. Eur. Phys. J. C 72, 2034 (2012). https://doi.org/10.1140/epjc/s10052-012-2034-x

    Article  ADS  MATH  Google Scholar 

  15. Haouat, S., Chekireb, R.: Effect of the electric field on the creation of fermions in de-Sitter space-time, (2015). https://doi.org/10.48550/arXiv.1504.08201

  16. Sogut, K., Havare, A.: On the scalar particle creation by electromagnetic fields in Robertson-Walker spacetime. Nucl. Phys. B 901, 76 (2015). https://doi.org/10.1016/j.nuclphysb.2015.10.005

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Rajeev, K., Chakraborty, S., Padmanabhan, T.: Generalized Schwinger effect and particle production in an expanding universe. Phys. Rev. D 100, 045019 (2019). https://doi.org/10.1103/PhysRevD.100.045019

    Article  ADS  MathSciNet  Google Scholar 

  18. Hamil, B., Merad, M., Birkandan, T.: Pair creation in curved Snyder space. Int. J. Mod. Phys. A 35, 2050014 (2020). https://doi.org/10.1142/S0217751X20500141

    Article  ADS  MathSciNet  Google Scholar 

  19. Pimentel, L.O., Pineda, F.: Particle creation in some LRS Bianchi I models. Gen Relativ Gravit 53, 62 (2021). https://doi.org/10.1007/s10714-021-02828-w

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Pieper, W., Greiner, W.: Interior electron shells in superheavy nuclei. Z. Physik 218, 327 (1969). https://doi.org/10.1007/BF01670014

    Article  ADS  Google Scholar 

  21. Gershtein, S.S., Zeldovich, Y.B.: Positron Production during the Mutual Approach of Heavy Nuclei and the Polarization of the Vacuum, Sov. Phys. JETP 30, 358 (1970). http://jetp.ras.ru/cgi-bin/e/index/e/30/2/p358?a=list

  22. Popov, V.S.: Positron production in a Coulomb Field with Z \(>\) 137, Sov. Phys. JETP, 32, 526 (1971). http://www.jetp.ras.ru/cgi-bin/dn/e_032_03_0526.pdf

  23. Rafelski, J., Fulcher, L.P., Klein, A.: Fermions and bosons interacting with arbitrarily strong external fields. Phys. Rep. 38, 227 (1978). https://doi.org/10.1016/0370-1573(78)90116-3

    Article  ADS  Google Scholar 

  24. Soffel, M., Muller, B., Greiner, W.: Stability and decay of the Dirac vacuum in external gauge fields. Phys. Rep. 85, 51 (1982). https://doi.org/10.1016/0370-1573(82)90129-6

    Article  ADS  MathSciNet  Google Scholar 

  25. B\(\breve{a}\)loi, M.A.: The production of particles with well determined angular momentum in external Coulomb field on de Sitter expanding universe, Nucl. Phys. B 980, 115796 (2022). https://doi.org/10.1016/j.nuclphysb.2022.115796

  26. Popov, V.S.: Critical charge in quantum electrodynamics. Phys. Atom. Nuclei 64, 367 (2001). https://doi.org/10.1134/1.1358463

    Article  ADS  Google Scholar 

  27. Rafelski, J., Kirsch, J., Müller, B., Reinhardt, J., Greiner, W.: Probing QED Vacuum with Heavy Ions. In: Schramm, S., Schäfer, M. (eds.) New Horizons in Fundamental Physics. FIAS Interdisciplinary Science Series. Springer (2017), pp 211-251. https://doi.org/10.1007/978-3-319-44165-8_17[CrossRef]

  28. Voskresensky, D.N.: Electron-Positron Vacuum Instability in Strong Electric Fields. Relativistic Semiclassical Approach, Universe 7, 104 (2021). https://doi.org/10.3390/universe7040104

    Article  Google Scholar 

  29. Pullin, J., Verdaguer, E.: Gravitational particle production in the formation of global monopoles and domain walls. Phys. Lett. B 246, 371 (1990). https://doi.org/10.1016/0370-2693(90)90616-E

    Article  ADS  Google Scholar 

  30. Duru, I.H.: Spontaneous pair production in a magnetic monopole field. J. Phys. A: Math. Gen. 28, 5883 (1995). https://doi.org/10.1088/0305-4470/28/20/017

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Parker, L.: Gravitational particle production in the formation of cosmic strings. Phys. Rev. Lett. 59, 1369 (1987). https://doi.org/10.1103/PhysRevLett.59.1369

    Article  ADS  Google Scholar 

  32. Sahni, V.: Particle creation by cosmic strings. Mod. Phys. Lett. A 3, 1425 (1988). https://doi.org/10.1142/S0217732388001719

    Article  ADS  Google Scholar 

  33. Mendell, G., Hiscock, W.A.: Gravitational particle production during cosmic-string formation in the sudden approximation. Phys. Rev. D 40, 282 (1989). https://doi.org/10.1103/PhysRevD.40.282

    Article  ADS  Google Scholar 

  34. Harari, D.D., Skarzhinsky, V.D.: Pair production in the gravitational field of a cosmic string. Phys. Lett. B 240, 322 (1990). https://doi.org/10.1016/0370-2693(90)91106-L

    Article  ADS  Google Scholar 

  35. Garriga, J., Harari, D., Verdaguer, E.: Gravitational particle production by cosmic strings. Nucl. Phys. B 339, 560 (1990). https://doi.org/10.1016/0550-3213(90)90362-H

    Article  ADS  Google Scholar 

  36. Jensen, B.: Production of quantum particles on cones. Phys. Scr. 45, 548 (1992). https://doi.org/10.1088/0031-8949/45/6/002

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Brevik, I., Toverud, T.: Electromagnetic energy production in the formation of a superconducting cosmic string. Phys. Rev. D 51, 691 (1995). https://doi.org/10.1103/PhysRevD.51.691

    Article  ADS  MATH  Google Scholar 

  38. De Lorenci, V.A., De Paola, R., Svaiter, N.F.: Gravitational Particle Production in Spinning Cosmic String Spacetimes, Nuovo Cim. B 113, 1331 (1998). https://arxiv.org/abs/gr-qc/9705049

  39. De Lorenci, V.A., De Paola, R., Svaiter, N.F.: From spinning to non-spinning cosmic string spacetime. Class. Quantum Grav. 16, 3047 (1999). https://doi.org/10.1088/0264-9381/16/10/302

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. Bezerra, V.B., Mostepanenko, V.M., Teixeira Filho, R.M.: Particle creation in the chiral cosmic string spacetime. Int. J. Mod. Phys. D 11, 437 (2002). https://doi.org/10.1142/S0218271802001718

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Kibble, T.W.B.: Topology of cosmic domains and strings. J. Phys. A 9, 1387 (1976). https://doi.org/10.1088/0305-4470/9/8/029

    Article  ADS  MATH  Google Scholar 

  42. Zeldovich, Y.B.: Cosmological fluctuations produced near a singularity. Mon. Not. R. Astron. Soc. 192, 663 (1980). https://doi.org/10.1093/mnras/192.4.663

    Article  ADS  Google Scholar 

  43. Vilenkin, A., Shellard, E.P.: Cosmic Strings and Other Topological Defects. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  44. Gott, J.R., III.: Gravitational lensing effects of vacuum strings - Exact solutions. Astrophys. J. 288, 422 (1985). https://doi.org/10.1086/162808

    Article  ADS  MathSciNet  Google Scholar 

  45. Linet, B.: A vortex-line model for infinite straight cosmic strings. Phys. Lett. A 124, 240 (1987). https://doi.org/10.1016/0375-9601(87)90629-3

    Article  ADS  MathSciNet  Google Scholar 

  46. Linet, B.: Force on a charge in the space-time of a cosmic string. Phys. Rev. D 33, 1833 (1986). https://doi.org/10.1103/PhysRevD.33.1833

    Article  ADS  Google Scholar 

  47. Bezerra de Mello, E.R., Bezerra, V.B., Furtado, C., Moraes, F.: Self-forces on electric and magnetic linear sources in the space-time of a cosmic string. Phys-Rev. D 51, 7140 (1995). https://doi.org/10.1103/Phys-RevD.51.7140

  48. Smith, A.G.: Gravitational effects of an infinite straight cosmic string on classical and quantum fields: Self-forces and vacuum fluctuations. In: Gibbons, G.W., Hawking, S.W., Vachaspati, T. (eds.) The Formation and Evolution of Cosmic Strings, pp. 263–292. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  49. Dowker, J.S.: Casimir effect around a cone. Phys. Rev. D 36, 3095 (1987). https://doi.org/10.1103/PhysRevD.36.3095

    Article  ADS  Google Scholar 

  50. Dowker, J.S.: A gravitational Aharonov-Bohm effect. Nuovo Cimento B 52, 129 (1967). https://doi.org/10.1007/BF02710657

    Article  ADS  Google Scholar 

  51. Planck Collaboration, Ade, P., et al.: Planck 2013 results. XXV. Searches for cosmic strings and other topological defects, (2013). Astron. Astrophys. 571, A25 (2014).https://doi.org/10.1051/0004-6361/201321621

  52. Sakellariadou, M.: Gravitational waves emitted from infinite strings, Phys. Rev. D 42, 354 (1990), https://doi.org/10.1103/PhysRevD.42.354. Erratum Phys. Rev. D 43, 4150 (1991), https://doi.org/10.1103/PhysRevD.43.4150.2

  53. Damour, T., Vilenkin, A.: Gravitational Wave Bursts from Cosmic Strings. Phys. Rev. Lett. 85, 3761 (2000). https://doi.org/10.1103/PhysRevLett.85.3761

    Article  ADS  Google Scholar 

  54. Blasi, S., Brdar, V., Schmitz, K.: Has NANOGrav Found First Evidence for Cosmic Strings? Phys. Rev. Lett. 126, 041305 (2021). https://doi.org/10.1103/PhysRevLett.126.041305

    Article  ADS  MathSciNet  Google Scholar 

  55. Boileau, G., Jenkins, A.C., Sakellariadou, M., Meyer, R., Christensen, N.: Ability of LISA to detect a gravitational-wave background of cosmological origin: The cosmic string case. Phys. Rev. D 105, 023510 (2022). https://doi.org/10.1103/PhysRevD.105.023510

    Article  ADS  Google Scholar 

  56. Battacharjee, P., Sigl, G.: Origin and propagation of extremely high-energy cosmic rays. Phys. Rep. 327, 109 (2000). https://doi.org/10.1016/S0370-1573(99)00101-5

    Article  ADS  Google Scholar 

  57. Yang, Y., Jing, J., Tian, Z.: Probing cosmic string spacetime through parameter estimation. Eur. Phys. J. C 82, 688 (2022). https://doi.org/10.1140/epjc/s10052-022-10628-y

    Article  ADS  Google Scholar 

  58. Anderson, M.R., Moraes, F.: The mathematical theory of cosmic strings. IOP Publishing, Bristol (2003). (Chapter 7)

    Book  Google Scholar 

  59. Sokoloff, D.D., Starobinskii, A.A.: On the structure of curvature tensor on conical singularities, Dokl. Akad. Nauk SSSR, 234, 1043 (1977) [Sov. Phys. Dokl. 22, 312 (1977)]. http://mi.mathnet.ru/eng/dan/v234/i5/p1043

  60. Katanaev, M.O., Volovich, I.V.: Theory of defects in solids and three-dimensional gravity. Annals of Physics 216, 1 (1992). https://doi.org/10.1016/0003-4916(52)90040-7

    Article  ADS  MathSciNet  MATH  Google Scholar 

  61. Furtado, C., Moraes, F.: On the binding of electrons and holes to disclinations. Physics Letters A 188, 394 (1994). https://doi.org/10.1016/0375-9601(94)90482-0

    Article  ADS  Google Scholar 

  62. Voronov, B.L., Gitman, D.M., Tyutin, I.V.: The Dirac Hamiltonian with a superstrong Coulomb field. Theor. Math. Phys. 150, 34 (2007). https://doi.org/10.1007/s11232-007-0004-5

    Article  MathSciNet  MATH  Google Scholar 

  63. Al-Hashimi, M.H., Wiese, U.-J.: Self-adjoint extensions for confined electrons: From a particle in a spherical cavity to the hydrogen atom in a sphere and on a cone. Ann. Phys. 327, 2742 (2012). https://doi.org/10.1016/j.aop.2012.06.006

    Article  ADS  MATH  Google Scholar 

  64. Cruz Neto, F.A., da Silva, F.M., Santos, L.C.N., Castro, L.B.: Scalar bosons with Coulomb potentials in a cosmic string background: scattering and bound states, Eur. Phys. J. Plus, 135: 25 (2020). https://doi.org/10.1140/epjp/s13360-019-00062-7

  65. Olver, F.W.J., Lozier, D.W., Boisvert, R.F., Clark, C.W.: NIST Handbook of Mathematical Functions, pp. 334–335. Cambridge University Press, Cambridge (2010)

    MATH  Google Scholar 

  66. Kim, S.P., Page, D.N.: Remarks on Schwinger Pair Production by Charged Black Holes. Nuovo Cim. B 120, 1193 (2005). https://doi.org/10.1393/ncb/i2005-10148-6

    Article  ADS  Google Scholar 

  67. de A. Marques, G., Bezerra, V.B.: Hydrogen atom in the gravitational fields of topological defects, Phys. Rev. D 66, 105011 (2002). https://doi.org/10.1103/PhysRevD.66.105011

  68. Hosseinpour, M., Hassanabadi, H.: Scattering states of Dirac equation in the presence of cosmic string for Coulomb interaction. Int. J. Mod. Phys. A 30, 1550124 (2015). https://doi.org/10.1142/S0217751X15501249

    Article  ADS  MathSciNet  MATH  Google Scholar 

  69. Marques, G.A., Bezerra, V.B., Fernandes, S.G.: Exact solution of the Dirac equation for a Coulomb and scalar potentials in the gravitational field of a cosmic string. Phys. Lett. A 341, 39 (2005). https://doi.org/10.1016/j.physleta.2005.04.031

    Article  ADS  MATH  Google Scholar 

  70. Greiner, W., Mulller, B., Rafelski, J.: Quantum Electrodynamics of Strong Fields, Springer, Berlin (1985). pp 71-73 and 86-89

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Acknowledgements

This research is supported by the Algerian Ministry of Higher Education and Scientific Research under the PRFU Project Number: B00L02UN180120210003.

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  1. Laboratory of Theoretical Physics, Department of Physics, University of Jijel, Jijel, 18000, Algeria

    B. Belbaki & A. Bounames

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BB done the main manuscript calculations and prepared figures; AB supervised the work, developed the studies and corrections. All authors reviewed the manuscript.

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Belbaki, B., Bounames, A. Influence of a Cosmic String on the Rate of Pairs Produced by the Coulomb Potential. Int J Theor Phys 62, 136 (2023). https://doi.org/10.1007/s10773-023-05375-z

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