Colapso gravitacional de fluido perfeito em espaços-tempos circularmente simétricos com auto-similaridade cinemática - Miguelote, Alexandre Yasuda (2009)
Perfect fluid with kinematic self-similarity is studied in 2 + 1 dimensional spacetimes with circular symmetry and various exact solutions to the Einstein field equations are given. These include all the solutions of dust and stiff perfect fluid with self-similarity of the first kind (homothetic) and all the solutions of perfect fluid with a linear equation of state and self-similarity of the zeroth and second kinds. It is found that some of these solutions represent gravitational collapse and the final state of the collapse can be either a black hole or a null singularity. It is also shown that one solution can have two different kinds of kinematic self-similarity. At last, linear perturbations of homothetic self-similar stiff fluid solutions are studied. It is found that, except for those with n = 1 and n = 3, none of them is stable and all have more than one unstable mode. Hence, none of these solutions can be critical, because, by definition, a critical solution has one and only one unstable mode.