Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 72, p. 39-43 (2025)
CIRCULAR ORBITS AROUND STATIC SPHERICALLY SYMMETRIC CONFIGURATION WITH LINEAR MASSIVE SCALAR FIELD IN GENERAL RELATIVITY
Valery ZHDANOV, DSc (Phys. & Math.), Prof.
ORCID ID: 0000-0003-3690-483X
е-mail: Valery.Zhdanov@knu.ua
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
Denys TVARDOVSKY, Student
ORCID ID: 0009-0002-1031-0208
e-mail: twardowski@knu.ua
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
Abstract
Background. Theories with scalar fields are widely discussed in various generalizations of the Standard cosmological model dealing with the inflation of the Universe, dynamical dark energy, Hubble tension etc. Introduction of a scalar field in static spherically symmetric (SSS) asymptotically flat gravitational system causes the appearance of specific features in the distribution of stable circular orbits, which may lead to observational effects in the accretion disk structure. We study this distribution in the case of a massive scalar field in the framework of General Relativity.
Methods. We consider the Einstein equations with minimally coupled massive scalar field resulting in the ordinary differential system that is solved numerically (SSS case). This solution is applied to study the distribution of stable circular orbits of test bodies using properties of an effective potential for the test-body motion.
Results. There are two main regions around the asymptotically flat SSS configuration with scalar field: a weak-field region, where we have an approximate analytical description of the problem and usual distribution of circular orbits as in case of the Schwarzschild metric, and a scalarization region with a significant deviation of the metric from the Schwarzschild case. In the scalarization region, a numerical solution for the linear scalar field with the corresponding metric coefficients is derived. Analytical relations to study the test body circular orbits are obtained. We show that, for a wide range of masses of the linear scalar field and astrophysically relevant configuration masses, there either exists a region of weakly stable circular orbits near the center, or there are no circular orbits in the scalarization region at all.
Conclusions. The distribution of stable circular orbits is significantly different from the case of a Schwarzschild black hole. In case of sufficiently large masses of the scalar field and configuration masses, the circular orbits in the scalarization region will be virtually absent. This suggest a similar conclusion about the structure of accretion disks.
Key words
Elativistic objects, naked singularities, modified gravity.
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DOI: https://doi.org/10.17721/BTSNUA.2025.72.39-43