Advertisement

Scattering of uncharged particles in the field of two extremely charged black holes

  • Donato Bini
  • Andrea GeralicoEmail author
  • Gabriele Gionti
  • Wolfango Plastino
  • Nelson Velandia
Research Article
  • 49 Downloads

Abstract

We investigate the motion of uncharged particles scattered by a binary system consisting of extremely charged black holes in equilibrium as described by the Majumdar–Papapetrou solution. We focus on unbound orbits confined to the plane containing both black holes. We consider the two complementary situations of particles approaching the system along a direction parallel to the axis where the black holes are displaced and orthogonal to it. We numerically compute the scattering angle as a function of the particle’s conserved energy parameter, which provides a gauge-invariant information of the scattering process. We also study the precession of a test gyroscope along such orbits and evaluate the accumulated precession angle after a full scattering, which is another gauge-invariant quantity.

Keywords

Particle scattering Majumdar–Papapetrou spacetime Gyroscope precession 

Notes

Acknowledgements

We thank Prof. O. Semerák for useful discussions.

References

  1. 1.
    Bini, D., Damour, T.: Gravitational scattering of two black holes at the fourth post-Newtonian approximation. Phys. Rev. D 96(6), 064021 (2017).  https://doi.org/10.1103/PhysRevD.96.064021. [arXiv:1706.06877 [gr-qc]]ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Bel, L., Damour, T., Deruelle, N., Ibanez, J., Martin, J.: Poincaré-invariant gravitational field and equations of motion of two pointlike objects: the postlinear approximation of general relativity. Gen. Relativ. Gravit 13, 963 (1981).  https://doi.org/10.1007/BF00756073 ADSCrossRefGoogle Scholar
  3. 3.
    Westpfahl, K.: High-speed scattering of charged and uncharged particles in general relativity. Fortsch. Phys. 33, 417 (1985).  https://doi.org/10.1002/prop.2190330802 ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Damour, T.: Gravitational scattering, post-Minkowskian approximation and effective one-body theory. Phys. Rev. D 94(10), 104015 (2016).  https://doi.org/10.1103/PhysRevD.94.104015. [arXiv:1609.00354 [gr-qc]]ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Bini, D., Damour, T.: Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory. Phys. Rev. D 96(10), 104038 (2017).  https://doi.org/10.1103/PhysRevD.96.104038. [arXiv:1709.00590 [gr-qc]]ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Bini, D., Damour, T.: Gravitational spin-orbit coupling in binary systems at the second post-Minkowskian approximation. Phys. Rev. D 98(4), 044036 (2018).  https://doi.org/10.1103/PhysRevD.98.044036. [arXiv:1805.10809 [gr-qc]]ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Antonelli, A., Buonanno, A., Steinhoff, J., van de Meent, M., Vines, J.: Energetics of two-body Hamiltonians in post-Minkowskian gravity. Phys. Rev. D 99(10), 104004 (2019).  https://doi.org/10.1103/PhysRevD.99.104004. [arXiv:1901.07102 [gr-qc]]ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Damour, T., Jaranowski, P., Schäfer, G.: Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity. Phys. Rev. D 93(8), 084014 (2016). [arXiv:1601.01283 [gr-qc]]ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Bern, Z., Cheung, C., Roiban, R., Shen, C.H., Solon, M.P., Zeng, M.: Scattering amplitudes and the conservative hamiltonian for binary systems at third post-Minkowskian order. Phys. Rev. Lett. 122(20), 201603 (2019).  https://doi.org/10.1103/PhysRevLett.122.201603. [arXiv:1901.04424 [hep-th]]ADSCrossRefGoogle Scholar
  10. 10.
    Bern, Z., Cheung, C., Roiban, R., Shen, C.H., Solon, M.P., Zeng, M.: Black hole binary dynamics from the double copy and effective theory. J. High Energy Phys. 2019, 206 (2019).  https://doi.org/10.1007/JHEP10(2019)206. [arXiv:1908.01493 [hep-th]] ADSCrossRefGoogle Scholar
  11. 11.
    Detweiler, S.L.: Perspective on gravitational self-force analyses. Class. Quant. Grav. 22, S681 (2005).  https://doi.org/10.1088/0264-9381/22/15/006. [arXiv:gr-qc/0501004]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Foffa, S., Sturani, R.: Effective field theory methods to model compact binaries. Class. Quant. Grav. 31(4), 043001 (2014).  https://doi.org/10.1088/0264-9381/31/4/043001. [arXiv:1309.3474 [gr-qc]]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Buonanno, A., Damour, T.: Effective one-body approach to general relativistic two-body dynamics. Phys. Rev. D 59, 084006 (1999).  https://doi.org/10.1103/PhysRevD.59.084006. [arXiv:gr-qc/9811091]ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Buonanno, A., Damour, T.: Transition from inspiral to plunge in binary black hole coalescences. Phys. Rev. D 62, 064015 (2000).  https://doi.org/10.1103/PhysRevD.62.064015. [arXiv:gr-qc/0001013]ADSCrossRefGoogle Scholar
  15. 15.
    Bern, Z., Carrasco, J.J., Chen, W.M., Johansson, H., Roiban, R.: Gravity amplitudes as generalized double copies of Gauge-theory amplitudes. Phys. Rev. Lett. 118(18), 181602 (2017).  https://doi.org/10.1103/PhysRevLett.118.181602. [arXiv:1701.02519 [hep-th]]ADSCrossRefGoogle Scholar
  16. 16.
    Damour, T.: High-energy gravitational scattering and the general relativistic two-body problem. Phys. Rev. D 97(4), 044038 (2018).  https://doi.org/10.1103/PhysRevD.97.044038. [arXiv:1710.10599 [gr-qc]]ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Bini, D., Geralico, A.: Schwarzschild black hole embedded in a dust field: scattering of particles and drag force effects. Class. Quant. Grav. 33(12), 125024 (2016).  https://doi.org/10.1088/0264-9381/33/12/125024. [arXiv:1808.05826 [gr-qc]]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Bini, D., Geralico, A.: Scattering by a Schwarzschild black hole of particles undergoing drag force effects. Gen. Rel. Grav. 48(7), 101 (2016).  https://doi.org/10.1007/s10714-016-2094-6. [arXiv:1808.05825 [gr-qc]]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Bini, D., Geralico, A.: Hyperbolic-like elastic scattering of spinning particles by a Schwarzschild black hole. Gen. Relativ. Gravit 49(6), 84 (2017).  https://doi.org/10.1007/s10714-017-2247-2. [arXiv:1808.06502 [gr-qc]]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Bini, D., Geralico, A., Vines, J.: Hyperbolic scattering of spinning particles by a Kerr black hole. Phys. Rev. D 96(8), 084044 (2017).  https://doi.org/10.1103/PhysRevD.96.084044. [arXiv:1707.09814 [gr-qc]]ADSCrossRefGoogle Scholar
  21. 21.
    Bini, D., Geralico, A.: High-energy hyperbolic scattering by neutron stars and black holes. Phys. Rev. D 98(2), 024049 (2018).  https://doi.org/10.1103/PhysRevD.98.024049. [arXiv:1806.02085 [gr-qc]]ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Hartle, J.B., Hawking, S.W.: Solutions of the Einstein–Maxwell equations with many black holes. Commun. Math. Phys. 26, 87 (1972).  https://doi.org/10.1007/BF01645696 ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Shipley, J., Dolan, S.R.: Binary black hole shadows, chaotic scattering and the Cantor set. Class. Quant. Grav. 33(17), 175001 (2016).  https://doi.org/10.1088/0264-9381/33/17/175001. [arXiv:1603.04469 [gr-qc]]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Assumpcao, T., Cardoso, V., Ishibashi, A., Richartz, M., Zilhao, M.: Black hole binaries: ergoregions, photon surfaces, wave scattering, and quasinormal modes. Phys. Rev. D 98(6), 064036 (2018).  https://doi.org/10.1103/PhysRevD.98.064036. [arXiv:1806.07909 [gr-qc]]ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    Wunsch, A., Müller, T., Weiskopf, D., Wunner, G.: Circular orbits in the extreme Reissner–Nordstrøm dihole metric. Phys. Rev. D 87(2), 024007 (2013).  https://doi.org/10.1103/PhysRevD.87.024007. [arXiv:1301.7560 [gr-qc]]ADSCrossRefGoogle Scholar
  26. 26.
    Ryzner, J., Zofka, M.: Electrogeodesics in the di-hole Majumdar–Papapetrou spacetime. Class. Quant. Grav. 32(20), 205010 (2015).  https://doi.org/10.1088/0264-9381/32/20/205010. [arXiv:1510.02314 [gr-qc]]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Semerák, O., Basovník, M.: Geometry of deformed black holes. I. Majumdar–Papapetrou binary. Phys. Rev. D 94(4), 044006 (2016).  https://doi.org/10.1103/PhysRevD.94.044006. [arXiv:1608.05948 [gr-qc]]ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Jantzen, R.T., Carini, P., Bini, D.: The many faces of gravitoelectromagnetism. Ann. Phys. 215, 1 (1992).  https://doi.org/10.1016/0003-4916(92)90297-Y. [arXiv:gr-qc/0106043]ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Bini, D., Cherubini, C., Jantzen, R.T., Miniutti, G.: The Simon and Simon–Mars tensors for stationary Einstein–Maxwell fields. Class. Quant. Grav. 21, 1987 (2004).  https://doi.org/10.1088/0264-9381/21/8/005. [arXiv:gr-qc/0403022]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Baker, J.G., Campanelli, M.: Making use of geometrical invariants in black hole collisions. Phys. Rev. D 62, 127501 (2000).  https://doi.org/10.1103/PhysRevD.62.127501. [arXiv:gr-qc/0003031]ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Chandrasekhar, S.: The two center problem in general relativity: the scattering of radiation by two extreme Reissner–Nordstrom black holes. Proc. R. Soc. Lond. A 421, 227 (1989).  https://doi.org/10.1098/rspa.1989.0010 ADSCrossRefzbMATHGoogle Scholar
  32. 32.
    Contopoulos, G.: Periodic orbits and chaos around two black holes. Proc. R. Soc. Lond. A 431, 183 (1990).  https://doi.org/10.1098/rspa.1990.0126 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Contopoulos, G.: Periodic orbits and chaos around two fixed black holes. II. Proc. R. Soc. Lond. A 435, 551 (1991).  https://doi.org/10.1098/rspa.1991.0160 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Contopoulos, G., Papadaki, H.: Newtonian and relativistic periodic orbits around two fixed black holes. Celest. Mech. Dyn. Astron. 55, 47 (1993).  https://doi.org/10.1007/BF00694394 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Bernard, L., Cardoso, V., Ikeda, T., Zilhao, M.: Physics of black hole binaries: geodesics, relaxation modes, and energy extraction. Phys. Rev. D 100(4), 044002 (2019).  https://doi.org/10.1103/PhysRevD.100.044002. [arXiv:1905.05204 [gr-qc]]ADSCrossRefGoogle Scholar
  36. 36.
    Dettmann, C.P., Frankel, N.E., Cornish, N.J.: Fractal basins and chaotic trajectories in multi—black hole space-times. Phys. Rev. D 50, R618 (1994).  https://doi.org/10.1103/PhysRevD.50.R618. [arXiv:gr-qc/9402027]ADSCrossRefGoogle Scholar
  37. 37.
    Yurtsever, U.: Geometry of chaos in the two center problem in general relativity. Phys. Rev. D 52, 3176 (1995).  https://doi.org/10.1103/PhysRevD.52.3176. [arXiv:gr-qc/9412031]ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    Dettmann, C.P., Frankel, N.E., Cornish, N.J.: Chaos and fractals around black holes. Fractals 3, 161 (1995).  https://doi.org/10.1142/S0218348X9500014X. [arXiv:gr-qc/9502014]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Contopoulos, G., Voglis, N., Efthymiopoulos, C.: Chaos in relativity and cosmology. Celest. Mech. Dyn. Astron. 73, 1 (2003).  https://doi.org/10.1023/A:1008376523356 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Alonso, D., Ruiz, A., Sanchez-Hernandez, M.: Escape of photons from two fixed extreme Reissner–Nordstrom black holes. Phys. Rev. D 78, 104024 (2008).  https://doi.org/10.1103/PhysRevD.78.104024. [arXiv:gr-qc/0701052]ADSCrossRefGoogle Scholar
  41. 41.
    Iyer, B.R., Vishveshwara, C.V.: The Frenet–Serret description of gyroscopic precession. Phys. Rev. D 48, 5706 (1993).  https://doi.org/10.1103/PhysRevD.48.5706. [arXiv:gr-qc/9310019]ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Istituto per le Applicazioni del Calcolo “M. Picone,” CNRRomeItaly
  2. 2.INFN, Sezione di Roma TreRomeItaly
  3. 3.Specola VaticanaVatican CityVatican City State
  4. 4.Vatican Observatory Research Group Steward ObservatoryThe University of ArizonaTucsonUSA
  5. 5.INFN, Laboratori Nazionali di FrascatiFrascatiItaly
  6. 6.Department of Mathematics and PhysicsRoma Tre UniversityRomeItaly
  7. 7.Departamento de Fisica, Facultad de Ciencias PontificiaUniversidad JaverianaBogotá D. C.Colombia

Personalised recommendations