- 'A.N. Tsirulev'
date: 'Received: date / Accepted: date'
title: Bound orbits near scalar field naked singularities
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Introduction
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At present, we still do not exactly know the geometry of spacetime in the neighbourhood of the centre of normal galaxies. The best observational results have been obtained for the centres of our Galaxy and of M87 [@Meyer2012; @Akiyama2015; @Fish2016; @Gillessen2017; @Goddi2017; @Hees2017]. However, the available data are so far insufficient to identify these strongly gravitating objects and even to definitely distinguish between black holes, naked singularities, boson stars, and wormholes [@Joshi2014; @Macedo2013; @Li2014; @Grould2017a; @Grould2017b; @Abuter2018]. The EHT collaboration has recently observed [@Akiyama2018] the shadow, circled by a bright ring, in the centre of M87: this can be interpreted as the existence of closed photon orbits. However, it is shown in [@Shaikh2018] using a simple model that a naked singularity can have both a shadow and a photon sphere. In fact, observations of the orbits of stars near the centres have a key role in dealing with this question, but there are some obvious problems with the reasonable geometrical interpretation of such observations. First, one should not think of the central objects in galaxies as being in vacuum, because 