Growth of orbital resonances around a blackhole surrounded by matter

Proceedings of RAGtime / Growth of orbital resonances around a blackhole surrounded by matter

Growth of orbital resonances around a black hole surrounded by matter

Authors

Michal Stratený and Georgios Lukes-Gerakopoulos

Abstract

This work studies the dynamics of geodesic motion within a curved spacetime around a Schwarzschild black hole, perturbed by a gravitational field of a far axisymmetric distribution of mass enclosing the system. This spacetime can serve as a versatile model for a diverse range of astrophysical scenarios and, in particular, for extreme mass ratio inspirals as in our work. We show that the system is non-integrable by employing Poincaré surface of section and rotation numbers. By utilising the rotation numbers, the widths of resonances are calculated, which are then used in establishing the relation between the underlying perturbation parameter driving the system from integrability and the quadrupole parameter characterising the perturbed metric. This relation allows us to estimate the phase shift caused by the resonance during an inspiral.

Keywords

Geodesic motion – black holes – chaos

PDF file here

References

  1. Amaro-Seoane, P., Audley, H., Babak, S. et al. (LISA) (2017), Laser Interferometer Space Antenna, arXiv e-prints, arXiv: 1702.00786.
  2. Arnold, V. I. (1989), Mathematical Methods of Classical Mechanics, Springer, New York, first edition, ISBN 978-0387968902.
  3. Arnold, V. I., Kozlov, V. V. and Neishtadt, A. (2007), Mathematical Aspects of Classical and Celestial Mechanics, Encyclopaedia of Mathematical Sciences, Springer Berlin Heidelberg, ISBN 9783540489269.
  4. Babak, S., Gair, J., Sesana, A., Barausse, E., Sopuerta, C. F., Berry, C. P. L., Berti, E., Amaro-Seoane, P., Petiteau, A. and Klein, A. (2017), Science with the space-based interferometer lisa. v. extreme mass-ratio inspirals, Phys. Rev. D, 95, p. 103012, URL https://link.aps.org/doi/10.1103/PhysRevD.95.103012.
  5. Berry, C. P. L., Hughes, S. A., Sopuerta, C. F., Chua, A. J. K., Heffernan, A., Holley-Bockelmann, K., Mihaylov, D. P., Miller, M. C. and Sesana, A. (2019), The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy, arXiv: 1903.03686.
  6. Ferreira, M. C., Macedo, C. F. B. and Cardoso, V. (2017), Orbital fingerprints of ultralight scalar fields around black holes, Phys. Rev. D, 96, p. 083017, URL https://link.aps.org/doi/10.1103/PhysRevD.96.083017.
  7. Genzel, R., Eisenhauer, F. and Gillessen, S. (2010), The galactic center massive black hole and nuclear star cluster, Rev. Mod. Phys., 82, pp. 3121–3195, URL https://link.aps.org/doi/10.1103/RevModPhys.82.3121.
  8. Hannuksela, O. A., Ng, K. C. Y. and Li, T. G. F. (2020), Extreme dark matter tests with extreme mass ratio inspirals, Phys. Rev. D, 102, p. 103022, URL https://link.aps.org/doi/10.1103/PhysRevD.102.103022.
  9. Iro, H. (2016), Modern Approach To Classical Mechanics, World Scientific Publishing Co. Pte. Ltd., Singapore, second edition, ISBN 978-9814704113.
  10. Kerachian, M., Polcar, L., Skoupý, V., Efthymiopoulos, C. and Lukes-Gerakopoulos, G. (2023), Action-Angle formalism for extreme mass ratio inspirals in Kerr spacetime, arXiv e-prints, arXiv:2301.08150, arXiv: 2301.08150.
  11. Kerr, R. P. (1963), Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics, Physical Review Letters, 11(5), pp. 237–238.
  12. Lukes-Gerakopoulos, G. and Witzany, V. (2022), Nonlinear Effects in EMRI Dynamics and Their Imprints on Gravitational Waves, pp. 1625–1668, Springer Nature Singapore, Singapore, ISBN 978-981-16-4306-4, URL https://doi.org/10.1007/978-981-16-4306-4_42.
  13. Misner, C. W., Thorne, K. S. and Wheeler, J. A. (1973), Gravitation, W. H. Freeman, San Francisco, ISBN 978-0-7167-0344-0, 978-0-691-17779-3.
  14. Mukherjee, S., Kopáček, O. and Lukes-Gerakopoulos, G. (2023), Resonance crossing of a charged body in a magnetized Kerr background: An analog of extreme mass ratio inspiral, Physical Review D, 107(6), 064005, arXiv: 2206.10302.
  15. Polcar, L., Suková, P. and Semerák, O. (2019), Free Motion around Black Holes with Disks or Rings: Between Integrability and Chaos–V, Astrophys. J., 877(1), p. 16, arXiv: 1905.07646.
  16. Polcar, L. c. v., Lukes-Gerakopoulos, G. and Witzany, V. c. v. (2022), Extreme mass ratio inspirals into black holes surrounded by matter, Phys. Rev. D, 106, p. 044069, URL https://link.aps.org/doi/10.1103/PhysRevD.106.044069.
  17. Voglis, N., Contopoulos, G. and Efthymiopoulos, C. (1990), Detection of ordered and chaotic motion using the dynamical spectra, Impact of Modern Dynamics in Astronomy, Colloquium 172 of the Growth of orbital resonances around a black hole surrounded by matter 39 International Astronomical Union, 73, pp. 211–220.
  18. Zelenka, O., Lukes-Gerakopoulos, G., Witzany, V. and Kopáˇcek, O. (2020), Growth of resonances and chaos for a spinning test particle in the Schwarzschild background, Phys. Rev. D, 101(2), p. 024037, arXiv: 1911.00414.