Stability analysis of self-similar behaviors in perfect fluid gravitational collapse

Journal Article · Thu Jun 15 04:00:00 EDT 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.73.124030· OSTI ID:20774913

Mitsuda, Eiji; Tomimatsu, Akira ^[1]

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

Stability of self-similar solutions for gravitational collapse is an important problem to be investigated from the perspectives of their nature as an attractor, critical phenomena, and instability of a naked singularity. In this paper we study spherically symmetric non-self-similar perturbations of matter and metrics in spherically symmetric self-similar backgrounds. The collapsing matter is assumed to be a perfect fluid with the equation of state P={alpha}{rho}. We construct a single wave equation governing the perturbations, which makes their time evolution in arbitrary self-similar backgrounds analytically tractable. Further we propose an analytical application of this master wave equation to the stability problem by means of the normal mode analysis for the perturbations having the time dependence given by exp(i{omega}log vertical t vertical bar), and present some sufficient conditions for the absence of nonoscillatory unstable normal modes with purely imaginary {omega}.

• OSTI ID: 20774913
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 73; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ATTRACTORS
COSMOLOGY
DISTURBANCES
EINSTEIN FIELD EQUATIONS
EQUATIONS OF STATE
EVOLUTION
GRAVITATION
GRAVITATIONAL COLLAPSE
IDEAL FLOW
METRICS
NORMAL-MODE ANALYSIS
SINGULARITY
STABILITY
TIME DEPENDENCE
WAVE EQUATIONS