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)2270210.22363/2658-4670-2019-27-3-231-241Research ArticleGeodesic motion near self-gravitating scalar field configurationsPotashovIvan M.<p>Master of Science in Mathematics, Assistant of Department of General Mathematics and Mathematical Physics</p>potashov.im@tversu.ruTchemarinaJulia V.<p>Candidate of Physical and Mathematical Sciences, Assistant of professor of Department of General Mathematics and Mathematical Physics</p>chemarina.yv@tversu.ruTsirulevAlexander N.<p>Doctor of Physical and Mathematical Sciences, Professor of Department of General Mathematics and Mathematical Physics</p>tsirulev.an@tversu.ruTver State University1512201927323124122012020Copyright © 2019, Potashov I.M., Tchemarina J.V., Tsirulev A.N.2019<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 selfgravitating 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 depends 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>geodesicblack holenaked singularityscalar fieldгеодезическаячёрная дыраголая сингулярностьскалярное поле[The EHT collaboration, “First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole,” The Astrophysical Journal Letters, vol. 875, no. 1, 2019. DOI: 10.3847/2041-8213/ab0ec7.][R. Shaikh, P. Kocherlakota, R. Narayan, and P. S. Joshi, “Shadows of spherically symmetric black holes and naked singularities,” Monthly Notices of the Royal Astronomical Society, vol. 482, no. 1, pp. 52-64, 2018. DOI: 10.1093/mnras/sty2624.][V. I. Dokuchaev and Y. N. Eroshenko, “Weighing of the dark matter at the center of the Galaxy,” JETP Letters, vol. 101, no. 12, pp. 777-782, 2015. DOI: 10.1134/S0021364015120048.][A. Hees et al., “Testing General Relativity with stellar orbits around the supermassive black hole in our Galactic center,” Physycal Review Letters, vol. 118, no. 22, p. 211 101, 2017. DOI: 10.1103/PhysRevLett. 118.211101.][A. V. Zakharov, “Constraints on tidal charge of the supermassive black hole at the Galactic Center with trajectories of bright stars,” European Physical Journal C, vol. 78, p. 689, 2018. DOI: 10.1140/epjc/s10052018-6166-5.][M. De Laurentis, Z. Younsi, O. Porth, Y. Mizuno, and L. Rezzolla, “Test-particle dynamics in general spherically symmetric black hole spacetimes,” Physical Review D, vol. 97, no. 10, p. 104 024, 2018. DOI: 10.1103/PhysRevD.97.104024.][G. Z. Babar, A. Z. Babar, and Y. K. Lim, “Periodic orbits around a spherically symmetric naked singularity,” Physical Review D, vol. 96, no. 8, p. 084 052, 2017. DOI: 10.1103/PhysRevD.96.084052.][I. M. Potashov, J. V. Tchemarina, and A. N. Tsirulev, “Bound orbits near scalar field naked singularities,” European Physical Journal C, vol. 79, p. 709, 2019. DOI: 10.1140/epjc/s10052-019-7192-7.][K. A. Bronnikov and G. N. Shikin, “Spherically symmetric scalar vacuum: no-go theorems, black holes and solitons,” Gravitation and Cosmology, vol. 8, pp. 107-116, 2002.][V. V. Nikonov, J. V. Tchemarina, and A. N. Tsirulev, “A two-parameter family of exact asymptotically flat solutions to the Einstein-scalar field equations,” Classical and Quantum Gravity, vol. 25, no. 13, p. 138 001, 2008. DOI: 10.1088/0264-9381/25/13/138001.][J. V. Tchemarina and A. N. Tsirulev, “Spherically symmetric gravitating scalar fields. The inverse problem and exact solutions,” Gravitation and Cosmology, vol. 15, pp. 94-95, 2009.][M. Azreg-Ainou, “Selection criteria for two-parameter solutions to scalar-tensor gravity,” General Relativity and Gravitation, vol. 42, no. 6, pp. 1427-1456, 2010. DOI: 10.1007/s10714-009-0915-6.][D. A. Solovyev and A. N. Tsirulev, “General properties and exact models of static selfgravitating scalar field configurations,” Classical and Quantum Gravity, vol. 29, no. 5, p. 055 013, 2012. DOI: 10.1088/02649381/29/5/055013.][P. V. Kratovitch, I. M. Potashov, J. V. Tchemarina, and A. N. Tsirulev, “Topological geons with self-gravitating phantom scalar field,” Journal of Physics: Conference Series, vol. 934, no. 1, p. 012 047, Dec. 2017. DOI: 10.1088/1742-6596/934/1/012047.][I. M. Potashov, J. V. Tchemarina, and A. N. Tsirulev, “Bound orbits near black holes with scalar hair,” Journal of Physics: Conference Series, vol. 1390, no. 1, p. 012 097, Nov. 2019. DOI: 10.1088/1742-6596/1390/ 1/012097.][S. Gillessen et al., “An update on monitoring stellar orbits in the galactic center,” The Astrophysical Journal, vol. 837, no. 1, p. 30, 2017. DOI: 10.3847/1538-4357/aa5c41.][C. Goddi et al., “BlackHoleCam: fundamental physics of the Galactic center,” International Journal of Modern Physics D, vol. 26, no. 2, p. 1 730 001, 2017. DOI: 10.1142/S0218271817300014.]