Breakdown of self-similar evolution in homogeneous perfect fluid collapse

Abstract

The stability analysis of self-similar solutions is an important approach to confirm whether they act as an attractor in general non-self-similar gravitational collapse. Assuming that the collapsing matter is a perfect fluid with the equation of state P = αρ, we study spherically symmetric non-self-similar perturbations in homogeneous self-similar collapse described by the flat Friedmann solution. In the low pressure approximation α ≪ 1, we analytically derive an infinite set of the normal modes and their growth (or decay) rate. The existence of one unstable normal mode is found to conclude that the self-similar behavior in homogeneous collapse of a sufficiently low pressure perfect fluid must terminate and a certain inhomogeneous density profile can develop with the lapse of time.

Tilted Cylindrically Symmetric Self-Similar Solutions

“…They concluded that this growth is possible in the sufficiently bounded regions surrounding the black hole. Mitsuda and Tomimatsu [7] investigated the stability of self-similar solutions of gravitational collapse from the perspective of their nature as an attractor. They studied the critical phenomena and stability of a naked singularity.…”