by the quadratures (\[F-xi\])–(\[V\]) and the conditions (\[phi\]) and (\[3m&lt;xi0\]), the metricfunction $A(r)$ has a global minimum in the interval $(0,\infty)$. If the condition (\[cond3\]) holds, this minimum is unique.

For simplicity, we will assume below that the metric function $A(r)$ *has exactly one minimum* at $r=r_0$.

It is shown in the next section that these propositions give us a key distinguishing feature of scalar field configurations; in particular, it determines different behaviours of bound orbits around SFNSs on the one hand and around SFBHs on the other.

Bound orbits {#Sec3}
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In any static, spherically symmetric spacetime a massive test particle has three integrals of motion. For the metric of the form (\[metric\]) they are $$\label{int-motion}
\frac{dt}{ds}=\frac{E}{A}\,,\quad
\frac{d\varphi}{ds}=\frac{J}{\,r^2}\,,\quad
\left(\frac{dr}{ds}\right)^{\!\!2}=  \mathrm{e}^{-2\Phi}\!\! \left(E^2- {V\vphantom{\underline{A}}}_{\!\!eff}\right),$$ $$\label{Veff}
{V\vphantom{\underline{A}}}_{\!\!eff}= A\!\left(1+\frac{\,J^2}{\,r^2}\right),$$ where $V\vphantom{\underline{A}}_{\!\!eff}$ is the effective potential, $E$ is the specific energy, and $J$ is the specific angular momentum of a massive test particle.

We note that $V_{eff}\rightarrow1$ as $r\rightarrow\infty$ for any value of $J$ and for any asymptotically flat spacetime, but the results obtained in Sect. \[Sec2\] show radically different behaviour of the effective potentials in the interior regions of SFBHs and SFNSs, which implies in turn a crucial distinction between geodesic structures of 