  Scalar-tensor~(ST) theories of gravity are natural phenomenological
extensions to general relativity. Although these theories are severely
constrained both by solar system experiments and by binary pulsar observations,
a large set of ST families remain consistent with these observations. Recent
work has suggested probing the unconstrained region of the parameter space of
ST theories based on the stability properties of highly compact neutron stars.
Here, the dynamical evolution of very compact stars in a fully nonlinear code
demonstrates that the stars do become unstable and that the instability, in
some cases, drives the stars to collapse. We discuss the implications of these
results in light of recent observations of the most massive neutron star yet
observed. In particular, such observations suggest that such a star would be
subject to the instability for a certain regime; its existence therefore
supports a bound on the ST parameter space.
