# Geodesic motion near self-gravitating scalar field configurations

**Authors:**Tsirulev A.^{1}-
**Affiliations:**- Tver State University

**Issue:**Vol 27, No 3 (2019)**Section:**Mathematical Modeling and Computational Physics**URL:**https://journals.rudn.ru/miph/article/view/22449

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## Full Text

## Abstract

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.**

Email: tsirulev.an@tversu.ru

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## References

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