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Geodesic dynamics in Chazy–Curzon spacetimes

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Abstract

In the last decades, the dynamical studies around compact objects became a subject of active research, partially motivated by the observed differences in the profiles of the gravitational waves depending on the dynamics of the system. In this work, via the Poincaré section method, we conduct a thorough numerical analysis of the dynamical behavior of geodesics around Chazy–Curzon metrics. As the main result, we find only regular motions for the geodesics in all cases, which suggest the existence of the so-called Carter’s constant in this kind of exact solutions. Moreover, our simulations indicate that in the two-particle Chazy–Curzon solution, some oscillatory motions take place as in the classical MacMillan problem.

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Notes

  1. At this point, it is important to note that such strut can be removed by adding spin to the sources, see e.g. [21, 22]; however, these metrics will be considered further in a forthcoming paper.

References

  1. E Poisson and C M Will Gravity: Newtonian, Post-Newtonian, Relativistic (Cambridge: Cambridge University Press) (2014)

    Book  Google Scholar 

  2. L Blanchet Comptes Rendus Acad. Sci. Ser. IV Phys. 2 1343 (2001)

    Google Scholar 

  3. R M Wald Phys. Rev. D 10 1680 (1974)

    Article  ADS  Google Scholar 

  4. V Paschalidis and S L Shapiro Phys. Rev. D 88 104031 (2013)

    Article  ADS  Google Scholar 

  5. J Chazy Bull. Soc. Math. Fr. 52 17 (1924)

    Article  Google Scholar 

  6. H E J Curzon Proc. Lond. Math. Soc. 2 477 (1925)

    Article  MathSciNet  Google Scholar 

  7. A Papapetrou Proc. R. Ir. Acad. Sect. A Math. Phys. Sci. 51 191 (1945)

    Google Scholar 

  8. S D Majumdar Phys. Rev. 72 390 (1947)

    Article  ADS  MathSciNet  Google Scholar 

  9. W B Bonnor Z. Phys. 190 444 (1966)

    Article  ADS  Google Scholar 

  10. J B Hartle and S W Hawking Commun. Math. Phys. 26 87 (1972)

    Article  ADS  Google Scholar 

  11. D Kramer and G Neugebauer Phys. Lett. A 75 259 (1980)

    Article  ADS  Google Scholar 

  12. R Emparan Phys. Rev. D 61 104009 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  13. V S Manko, R I Rabadán and J D Sanabria-Gómez Phys. Rev. D 89 064049 (2014)

    Article  ADS  Google Scholar 

  14. J B Griffiths and J Podolský Exact Space-Times in Einstein’s General Relativity (Cambridge: Cambridge University Press) (2009)

    Book  Google Scholar 

  15. A Einstein and N Rosen Phys. Rev. 49 404 (1936)

    Article  ADS  Google Scholar 

  16. M Abdelqader PhD thesis (Queen’s University, Canada) (2013)

  17. B Carter Phys. Rev. 174 1559 (1968)

    Article  ADS  Google Scholar 

  18. F L Dubeibe, L A Pachón and J D Sanabria-Gómez Phys. Rev. D 75 023008 (2007)

    Article  ADS  Google Scholar 

  19. N J Cornish Phys. Rev. D 64 084011 (2001)

    Article  ADS  Google Scholar 

  20. H Weyl Ann. Phys. 359 117 (1917)

    Article  Google Scholar 

  21. W Dietz and C Hoenselaers Proc. R. Soc. Lond. A 382 221 (1982)

    Article  ADS  Google Scholar 

  22. J L Hernández-Pastora, V S Manko and J Martn J. Math. Phys. 34 4760 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  23. C Hoenselaers and Z Perjes Class. Quantum Gravity7 1819 (1990)

    Article  ADS  Google Scholar 

  24. T P Sotiriou and T A Apostolatos Class. Quantum Gravity 21 5727 (2004)

    Article  ADS  Google Scholar 

  25. F L Dubeibe and J D Sanabria-Gómez Phys. Rev. D 94 044058 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  26. R Gautreau and J L Anderson Phys. Lett. A 25 291 (1967)

    Article  ADS  Google Scholar 

  27. L Herrera Found. Phys. Lett. 18 21 (2005)

    Article  MathSciNet  Google Scholar 

  28. W D MacMillan Astron. J. 27 11 (1911).

    Article  ADS  Google Scholar 

  29. P J Holmes and J E Marsden J. Math. Phys. 23 669 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  30. F L Dubeibe, F D Lora-Clavijo and G A González Phys. Lett. A 381 563 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  31. F L Dubeibe, F D Lora-Clavijo and G A González Astrophys. Space Sci. 362 97 (2017)

    Article  ADS  Google Scholar 

  32. E E Zotos and F L Dubeibe Int. J. Modern Phys. D 27 1850036 (2018)

    Article  ADS  Google Scholar 

  33. A E Motter Phys. Rev. Lett. 91 231101 (2003)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

One of the authors (FLD) gratefully acknowledges the financial support provided by Universidad de los Llanos and Colciencias (Colombia), under Grants Nos. 8840 and 8863.

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Authors and Affiliations

  1. Grupo de Investigación Cavendish, Facultad de Ciencias Humanas y de la Educación, Universidad de los Llanos, Villavicencio, 500017, Colombia

    F. L. Dubeibe

  2. Facultad de Ciencias Básicas e Ingeniería, Universidad de los Llanos, Villavicencio, 500017, Colombia

    J. D. Arias H.

  3. Departamento de FÍsica, Facultad de Ciencias, Universidad de los Andes, Bogotá, 111711, Colombia

    J. E. Alfonso

Authors
  1. F. L. Dubeibe
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  2. J. D. Arias H.
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  3. J. E. Alfonso
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Correspondence to F. L. Dubeibe.

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Dubeibe, F.L., Arias H., J.D. & Alfonso, J.E. Geodesic dynamics in Chazy–Curzon spacetimes. Indian J Phys 93, 1635–1641 (2019). https://doi.org/10.1007/s12648-019-01416-8

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