Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)22449Geodesic motion near self-gravitating scalar field configurationsTsirulevAlexander<p>Doctor of Physical and Mathematical Sciences, Professor of Department of General Mathematics and Mathematical Physics, Faculty of Mathematics</p>tsirulev.an@tversu.ruTver State University151220192731512201924122019Copyright © 2021, Tsirulev A.2021<p>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.</p>geodesic, black hole, naked singularity, scalar fieldгеодезическая, черная дыра, голая сингулярность, скалярное поле[1. K. Akiyama et al (The EHT collaboration), First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole. Astrophys.][J. Lett. 875, L1 (2019)][2. R. Shaikh, P. Kocherlakota, R. Narayan, P.S. Joshi, Shadows of spherically][symmetric black holes and naked singularities. Mon. Not. R. Astron. Soc.][482, 52–64 (2018)][3. V.I. Dokuchaev, Yu.N. Eroshenko, Weighing of the dark matter at the center][of the Galaxy. JETP Letters 101, 777–782 (2015)][4. A. Hees et al, Testing General Relativity with stellar orbits around the][supermassive black hole in our Galactic center. Phys. Rev. Lett. 118, 211101][(2017)I. Potashovov, J. Tchemarina, A. Tsirulev, 9][5. A.F. Zakharov, Constraints on tidal charge of the supermassive black hole][at the Galactic Center with trajectories of bright stars. Eur. Phys. J. C 78,][689 (2018)][6. M. De Laurentis, Z. Younsi, O. Porth, Y. Mizuno, L. Rezzolla, Test-particle][dynamics in general spherically symmetric black hole spacetimes. Phys. Rev.][D 97, 104024 (2018)][7. G.Z. Babar, A.Z. Babar, Y.K. Lim, Periodic orbits around a spherically][symmetric naked singularity. Phys. Rev. D 96, 084052 (2017)][8. I.M. Potashov, Ju.V. Tchemarina, A.N. Tsirulev, Bound orbits near scalar][field naked singularities. European Physical Journal C, 79:709 (2019)][9. K.A. Bronnikov, G.N. Shikin, Spherically symmetric scalar vacuum: no-go][theorems, black holes and solitons. Grav. Cosmol. 8, 107–116 (2002)][10. V.V Nikonov, Ju.V. Tchemarina, A.N. Tsirulev, A two-parameter family][of exact asymptotically flat solutions to the Einstein-scalar field equations.][Class. Quantum Grav. 25, 138001 (2008)][11. Ju.V. Tchemarina, A.N. Tsirulev, Spherically symmetric gravitating scalar][fields. The inverse problem and exact solutions. Gravitation and Cosmology][15, 94–95 (2009)][12. M. Azreg-Aïnou, Selection criteria for two-parameter solutions to scalartensor gravity. Gen. Rel. Grav. 42, 1427–1456 (2010)][13. D.A. Solovyev, A.N. Tsirulev, General properties and exact models of static][selfgravitating scalar field configurations. Class. Quantum Grav. 29, 055013][(2012)][14. P.V. Kratovitch, I.M. Potashov, Ju.V. Tchemarina, A.N. Tsirulev, Topological geons with self-gravitating phantom scalar field. Journal of Physics:][Conference Series 934, 012047 (2017)][15. I.M. Potashov, Ju.V. Tchemarina and A.N. Tsirulev. Bound orbits near][black holes with scalar hair. Journal of Physics, V. 1390, No 1, 012097][(2019)][16. S. Gillessen et al, An update on monitoring stellar orbits in the galactic][center. Astrophys. J. 837, 30 (2017)][17. C. Goddi et al, BlackHoleCam: fundamental physics of the Galactic center.][Int. J. Mod. Phys. D 26, 1730001 (2017)]