  Complete tensor-scalar and hydrodynamic equations are presented and
integrated, for a self-gravitating perfect fluid. The initial conditions
describe unstable-equilibrium neutron star configuration, with a polytropic
equation of state. They are necessary in order to follow the gravitational
collapse (including full hydrodynamics) of this star toward a black hole and to
study the resulting scalar gravitational wave. The amplitude of this wave, as
well as the radiated energy dramatically increase above some critical value of
the parameter of the coupling function, due to the spontaneous scalarization,
an effect not present in Brans-Dicke theory. In most cases, the pressure of the
collapsing fluid does not have a significant impact on the resulting signal.
These kind of sources are not likely to be observed by future laser
interferometric detectors (such as VIRGO or LIGO) of gravitational waves, if
they are located at more than a few 100 kpc. However, spontaneous scalarization
could be constrained if such a gravitational collapse is detected by its
quadrupolar gravitational signal, since this latter is quite lower than the
monopolar one.
