Resumo:
A gravitational collapse model is constructed by analyzing the evolution of a hypersurface
that separates two regions of a manifold. A Vaidya type metric is used for the exterior
region and for the interior region the Friedmann-Lemaître-Robertson-Walker (FLRW)
type of metric is taken, which are glued using the Darmois matching conditions. Initially,
the source of the curvature in the interior region is a scalar field non-minimally coupled
to the geometry, in such a way to produce a bouncing model that does not violate the
null energy condition, however it is obtained that this condition limits the model to the
minimun coupling situation. With this aim, it is made a power series approximation of the
system of equations formed by the Einstein field equations and the equation of the scalar
field close to the bounce. The results obtained for the coefficients and the validity of the
approximation itself reinforce the need for a positive spatial tri-curvature, whose value
is defined in the validity intervals obtained during the analysis of the parameters. Initial
conditions that characterize the collapse are also determined and conditions that allow
the identification of its final stage are studied, which may in the emission of the entirety
of the object mass as eletromagnetic radiation, that is, an evaporation, It is also possible
to obtain a singular model or even a bounce of the object itself.
