Gravitational Collapse of an Imperfect Non Adiabatic Fluid

We study the evolution of an anisotropic shear-free fluid with heat flux and kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming that the part of the tangential pressure which is explicitly time dependent of the fluid is zero and that the fluid moves along time-like geodesics. The energy conditions, geometrical and physical properties of the solutions are studied. The energy conditions are all satisfied at the beginning of the collapse but when the system approaches the singularity the energy conditions are violated, allowing for the appearance of an attractive phantom energy. We have found that, depending on the self-similar parameter $\alpha$ and the geometrical radius, they may represent a naked singularity. We speculate that the apparent horizon disappears due to the emergence of exotic energy at the end of the collapse, or due to the characteristics of null acceleration systems as shown by recent work.