  Low-energy thermal equilibrium states of strongly coupled ${\cal N}=4$
supersymmetric Yang-Mills (SYM) theory on a three-sphere are unstable with
respect to fluctuations breaking the global $SO(6)$ R-symmetry. Using the gauge
theory/gravity correspondence, a large class of initial conditions in the
R-symmetry singlet sector of the theory was been identified that fail to
thermalize \cite{Buchel:2013uba,Balasubramanian:2014cja}. A toy model
realization of such states is provided by {\it boson stars}, a stationary
gravitational configurations supported by a complex scalar field in
$AdS_5$-gravity. Motivated by the SYM example, we extend the boson star toy
model to include the global $SO(6)$ R-symmetry. We show that sufficient light
boson stars in the R-symmetry singlet sector are stable with respect to
linearized fluctuations. As the mass of the boson star increases, they do
suffer tachyonic instability associated with their localization on $S^5$. This
is opposite to the behaviour of small black holes (dual to equilibrium states
of ${\cal N}=4$ SYM) in global $AdS_5$: the latter develop tachyonic
instability as they become sufficiently light. Based on analogy with light
boson stars, we expect that the R-symmetry singlet nonthermal states in
strongly coupled gauge theories, represented by the quasiperiodic solutions of
\cite{Balasubramanian:2014cja}, are stable with respect to linearized
fluctuations breaking the R-symmetry.
