Breakdown of self-similar evolution in homogeneous perfect fluid collapse

Journal Article · Wed Nov 15 04:00:00 EST 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.74.104019· OSTI ID:20864127

Mitsuda, Eiji; Tomimatsu, Akira ^[1]

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1. Department of Physics, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602 (Japan)

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}<<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.

• OSTI ID: 20864127
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 74; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
ATTRACTORS
COSMOLOGY
DENSITY
DISTURBANCES
EQUATIONS OF STATE
GENERAL RELATIVITY THEORY
GRAVITATION
GRAVITATIONAL COLLAPSE
IDEAL FLOW
MATHEMATICAL SOLUTIONS
STABILITY