  In singularity generating spacetimes both the out-going and in-going
expansions of null geodesic congruences $\theta ^{+}$ and $\theta ^{-}$ should
become increasingly negative without bound, inside the horizon. This behavior
leads to geodetic incompleteness which in turn predicts the existence of a
singularity. In this work we inquire on whether, in gravitational collapse,
spacetime can sustain singularity-free trapped surfaces, in the sense that such
a spacetime remains geodetically complete. As a test case, we consider a well
known solution of the Einstien Field Equations which is Schwarzschild-like at
large distances and consists of a fluid with a $p=-\rho $ equation of state
near $r=0$. By following both the expansion parameters $\theta ^{+}$ and
$\theta ^{-}$ across the horizon and into the black hole we find that both
$\theta ^{+}$ and $\theta ^{+}\theta ^{-}$ have turning points inside the
trapped region. Further, we find that deep inside the black hole there is a
region $0\leq r<r_{0}$ (that includes the black hole center) which is not
trapped. Thus the trapped region is bounded both from outside and inside. The
spacetime is geodetically complete, a result which violates a condition for
singularity formation. It is inferred that in general if gravitational collapse
were to proceed with a $p=-\rho $ fluid formation, the resulting black hole may
be singularity-free.
