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

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dc.creatorMitsuda, Eiji
dc.creatorTomimatsu, Akira
dc.date2006-05-11
dc.date2006-06-22
dc.date.accessioned2026-07-07T07:09:43Z
dc.date.available2026-07-07T07:09:43Z
dc.descriptionStability 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 $P=αρ$. 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 $\exp{(iω\log|t|)}$, and present some sufficient conditions for the absence of non-oscillatory unstable normal modes with purely imaginary $ω$.
dc.description17 pages, 3 figures, matched to the published version
dc.identifierhttps://arxiv.org/abs/gr-qc/0605064
dc.identifierhttp://arxiv.org/abs/gr-qc/0605064
dc.identifierPhys.Rev. D73 (2006) 124030
dc.identifierdoi:10.1103/PhysRevD.73.124030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111175
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleStability analysis of self-similar behaviors in perfect fluid gravitational collapse
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