  It is well known that neutron stars can undergo a phase transition under a
certain class of Scalar Tensor Theories of gravity (STT's) where a new order
parameter, the {\it scalar charge}, appears within the star. This is the well
known phenomenon of spontaneous scalarization (SC) discovered by Damour and
Esposito-Far\`ese in 1993. Under such mechanism neutron stars can afford in
principle a maximum mass larger than in general relativity (GR) for a given
equation of state without taking into account additional observational
constraints (e.g. binary systems). This opens the possibility that neutron
stars might be formed with masses as large as $\sim 2 M_\odot$ without the need
of stiff, or more exotic, equations of state for the nuclear matter. Thus,
STT's through SC may account for compact objects with large masses observed
recently in the sky in the form of pulsars (PSR J0348+0432 with $M= 2.01 M_\pm
0.04\odot$ observed in 2013, PSR J1614-2230 with $M= 1.97\pm 0.04 M_\odot$
observed in 2010 or J0740+6620 $M= 2.14^{+0.10}_{-0.09} M_\odot$ observed in
2019). However, we argue that even if that was possible such maximum mass
models within STT cannot be formed solely from the dynamic transition of an
initial "isolated" unscalarized neutron star whose mass cannot exceed the
maximum mass in GR. This is because SC, being an energetic-preferred
configuration, produces a final static star with a mass lower that the initial
one with a fixed baryon mass. The mass difference between the initial and final
configurations is radiated away in the form of a scalar-field. Thus, maximum
mass models of scalarized neutron stars, if present in nature, must have formed
by a different process, perhaps of cosmological origin or by the subsequent
accretion of additional scalar charge and mass.
