  We obtain bounds on the stability of various self-gravitating astrophysical
objects using a new measure of shape complexity known as configurational
entropy. We apply the method to Newtonian polytropes, neutron stars with an
Oppenheimer-Volkoff equation of state, and to self-gravitating configurations
of complex scalar field (boson stars) with different self-couplings, showing
that the critical stability region of these stellar configurations obtained
from traditional perturbation methods correlates well with critical points of
the configurational entropy with accuracy of a few percent or better.
