Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 54, p. 35-38 (2016)

The body motion in gravitational field of a spherically symmetrical configuration with scalar field in General relativity

V. Zhdanov, Dr. Sci., Prof.
Astronomical Observatory of Taras Shevchenko National University of Kyiv,
O. Stashko, student, Physical Dept.
Taras Shevchenko National University of Kyiv
Abstract
We study exact special solutions of the joint system of Einstein equations and scalar field equations with a non-zero self-interaction potential, which describe spherically symmetric static configurations. The space-time is asymptotically flat with a naked singularity at the center. The testbody motion is analyzed; we found conditions for existence of non-connected regions of stable circular orbits. We show the existence of static trajectories of particles that hang above the configuration.

Keywords
Gravitational field, scalar field

References
Novosyadlyi, B., Pelykh, V., Shtanov, Yu., Zhuk, A. 2013, Dark energy and dark matter of the universe: in three volumes / Ed. V. Shulga, 1, Dark matter: Observational evidence and theoretical models, K.: Akademperiodyka, 380
Yatskiv, Ia. S., Aleksandrov, O. M., Vavylova, I. B. 2013, Zahalna teoriia vidnosnosti: horyzonty vyprobuvan, K.: VAITE, 264
Aleksandrov, A. N., Vavylova, Y. B., Zhdanov, V. Y. 2015, Obshchaia teoryia otnosytelnosty: pryznanye vremenem, K.: Naukova Dumka, 330
Fysher, Y. Z. 1948, ZhЭTF, 18, 636
Janis, A. I., Newman, E. T., Winicour, J. 1968, Phys. Rev. Lett., 20, 878
Chowdhury, A. N., Patil, M., Malafarina, D., Joshi, P. S. 2012, Phys. Rev. D. 85, id. 104031
Bronnykov, K.A., Rubyn, S.H. 2008, Lektsyy po hravytatsyy y kosmolohyy, M.: MYFY,460
Shikin, G. N., Bronnikov, K. A. 2002, Gravitation and Cosmology, 8, 107
Nikonov, V.V., Tchemarina, Ju.V., Tsirulev, A.N. 2008, Class. Quant. Grav., 25, id.138001
Solovyev, D., Tsirulev, A. 2012, Class. Quant. Grav., 29, id.055013
Felder, G., Frolov, A., Kofman, L., Linde, A. 2002, Phys. Rev. D., 66, id. 023507
Azreg-Aïnou, M. 2010, General Relativity and Gravitation, 42, 6, 1427
Guilbert, P.W., Rees, M.J. 1988, Mon. Notic. Roy. Astron. Soc., 233, 475
Lightman, A. P., White, T. R. 1988, Astrophys. J., 335, 57
Fabian, A. C., Rees, M. J., Stella, L. 1989, Mon. Notic. Roy. Astron. Soc., 238, 729
Vasylenko, A. A., Fedorova, E. V., Hnatyk, B. I., Zhdanov, V. I. 2015, Kinemat. Phys. Celest. Bodies., 31, 1, 13
Fedorova, E., Vasylenko, A., Hnatyk, B. I., Zhdanov, V. I. 2016, Astronom. Nachr., 337, 1–2, 96

Full text PDF

DOI: https://doi.org/10.17721/BTSNUA.2016.54.35-38