Gravitational collapse with tachyon field and barotropic fluid

A particular class of spacetime, with a tachyon field, \phi, and a barotropic fluid constituting the matter content, is considered herein as a model for gravitational collapse. For simplicity, the tachyon potential is assumed to be of inverse square form V(\phi)\sim \phi^{-2}. Our purpose, by making use of the specific kinematical features of the tachyon, which are rather different from a standard scalar field, is to establish the different types of asymptotic behavior that our matter content induces. Employing a dynamical system analysis, complemented by a thorough numerical study, we find classical solutions corresponding to a naked singularity or a black hole formation. In particular, there is a subset where fluid and tachyon participate in an interesting tracking behavior depending sensitively on the energy density initial profile of the tachyon field and barotropic fluid. We further complement our study by including linear tachyon fluctuations, which are coupled to metric perturbations. It is then shown that the tachyon perturbations can rapidly approach to zero (as the collapse proceeds).