Geodesic motion near self-gravitating scalar field configurations

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We study the geodesics motion of neutral test particles in the static spherically symmetric spacetimes of black holes and naked singularities supported by a self-gravitating real scalar field. The scalar field is supposed to model dark matter surrounding some strongly gravitating object such as the centre of our Galaxy. The behaviour of timelike and null geodesics very close to the centre of such a configuration crucially depend on the type of spacetime. It turns out that a scalar field black hole, analogously to a Schwarzschild black hole, has the innermost stable circular orbit and the (unstable) photon sphere, but their radii are always less than the corresponding ones for the Schwarzschild black hole of the same mass; moreover, these radii can be arbitrarily small. In contrast, a scalar field naked singularity has neither the innermost stable circular orbit nor the photon sphere. Instead, such a configuration has a spherical shell of test particles surrounding its origin and remaining in quasistatic equilibrium all the time. We also show that the characteristic properties of null geodesics near the centres of a scalar field naked singularity and a scalar field black hole of the same mass are qualitatively different.

About the authors

Alexander Tsirulev

Tver State University

Author for correspondence.

Doctor of Physical and Mathematical Sciences, Professor of Department of General Mathematics and Mathematical Physics, Faculty of Mathematics

Russian Federation, Faculty of Mathematics, Sadovyi per. 35, Tver, Russia, 170002


  1. K. Akiyama et al (The EHT collaboration), First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole. Astrophys.
  2. J. Lett. 875, L1 (2019)
  3. R. Shaikh, P. Kocherlakota, R. Narayan, P.S. Joshi, Shadows of spherically
  4. symmetric black holes and naked singularities. Mon. Not. R. Astron. Soc.
  5. , 52–64 (2018)
  6. V.I. Dokuchaev, Yu.N. Eroshenko, Weighing of the dark matter at the center
  7. of the Galaxy. JETP Letters 101, 777–782 (2015)
  8. A. Hees et al, Testing General Relativity with stellar orbits around the
  9. supermassive black hole in our Galactic center. Phys. Rev. Lett. 118, 211101
  10. (2017)I. Potashovov, J. Tchemarina, A. Tsirulev, 9
  11. A.F. Zakharov, Constraints on tidal charge of the supermassive black hole
  12. at the Galactic Center with trajectories of bright stars. Eur. Phys. J. C 78,
  13. (2018)
  14. M. De Laurentis, Z. Younsi, O. Porth, Y. Mizuno, L. Rezzolla, Test-particle
  15. dynamics in general spherically symmetric black hole spacetimes. Phys. Rev.
  16. D 97, 104024 (2018)
  17. G.Z. Babar, A.Z. Babar, Y.K. Lim, Periodic orbits around a spherically
  18. symmetric naked singularity. Phys. Rev. D 96, 084052 (2017)
  19. I.M. Potashov, Ju.V. Tchemarina, A.N. Tsirulev, Bound orbits near scalar
  20. field naked singularities. European Physical Journal C, 79:709 (2019)
  21. K.A. Bronnikov, G.N. Shikin, Spherically symmetric scalar vacuum: no-go
  22. theorems, black holes and solitons. Grav. Cosmol. 8, 107–116 (2002)
  23. V.V Nikonov, Ju.V. Tchemarina, A.N. Tsirulev, A two-parameter family
  24. of exact asymptotically flat solutions to the Einstein-scalar field equations.
  25. Class. Quantum Grav. 25, 138001 (2008)
  26. Ju.V. Tchemarina, A.N. Tsirulev, Spherically symmetric gravitating scalar
  27. fields. The inverse problem and exact solutions. Gravitation and Cosmology
  28. , 94–95 (2009)
  29. M. Azreg-Aïnou, Selection criteria for two-parameter solutions to scalartensor gravity. Gen. Rel. Grav. 42, 1427–1456 (2010)
  30. D.A. Solovyev, A.N. Tsirulev, General properties and exact models of static
  31. selfgravitating scalar field configurations. Class. Quantum Grav. 29, 055013
  32. (2012)
  33. P.V. Kratovitch, I.M. Potashov, Ju.V. Tchemarina, A.N. Tsirulev, Topological geons with self-gravitating phantom scalar field. Journal of Physics:
  34. Conference Series 934, 012047 (2017)
  35. I.M. Potashov, Ju.V. Tchemarina and A.N. Tsirulev. Bound orbits near
  36. black holes with scalar hair. Journal of Physics, V. 1390, No 1, 012097
  37. (2019)
  38. S. Gillessen et al, An update on monitoring stellar orbits in the galactic
  39. center. Astrophys. J. 837, 30 (2017)
  40. C. Goddi et al, BlackHoleCam: fundamental physics of the Galactic center.
  41. Int. J. Mod. Phys. D 26, 1730001 (2017)

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Copyright (c) 2021 Tsirulev A.

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