Breakdown of self-similar evolution in homogeneous perfect fluid collapse

Details Breakdown of self-similar evolution in homogeneous perfect fluid collapse Breakdown of self-similar evolution in homogeneous perfect fluid collapse

2006-10-10

arxiv.org/abs/gr-qc/0610042v2

Phys.Rev. D74 (2006) 104019

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, 1 figure, references added, published in Physical Review D

Scientific paper

10.1103/PhysRevD.74.104019

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 $P=\alpha\rho$, we study spherically symmetric non-self-similar perturbations in homogeneous self-similar collapse described by the flat Friedmann solution. In the low pressure approximation $\alpha \ll 1$, 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.

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