  A new model is proposed to a collapsing star consisting of an initial
inhomogeneous energy density and anisotropic pressure fluid with shear, radial
heat flow and outgoing radiation. In previous papers one of us has always
assumed an initial star with homogeneous energy density. The aim of this work
is to generalize the previous models by introducing an initial inhomogeneous
energy density and compare it to the initial homogeneous energy density
collapse model. We will show the differences between these models in the
evolution of all physical quantities that characterizes the gravitational
collapse. The behavior of the energy density, pressure, mass, luminosity and
the effective adiabatic index is analyzed. The pressure of the star, at the
beginning of the collapse, is isotropic but due to the presence of the shear
the pressure becomes more and more anisotropic. The black hole is never formed
because the apparent horizon formation condition is never satisfied, in
contrast of the previous model where a black hole is formed. An observer at
infinity sees a radial point source radiating exponentially until reaches the
time of maximum luminosity and suddenly the star turns off. In contrast of the
former model where the luminosity also increases exponentially, reaching a
maximum and after it decreases until the formation of the black hole. The
effective adiabatic index is always positive without any discontinuity in
contrast of the former model where there is a discontinuity around the time of
maximum luminosity. The collapse is about three thousand times slower than in
the case where the energy density is initially homogeneous.
