Critical phenomena and a new class of self-similar spherically symmetric perfect-fluid solutions

Abstract

We consider the self-similar solutions associated with the critical behavior observed in the gravitational collapse of spherically symmetric perfect fluids with equation of state $p=\alpha \mu$. We identify for the first time the global nature of these solutions and show that it is sensitive to the value of $\alpha$. In particular, for $\alpha >0.28$, we show that the critical solution is associated with a new class of asymptotically Minkowski self-similar spacetimes. We discuss some of the implications of this for critical phenomena.

5 pages RevTeX, 5 eps figures

References in corpus (4)

• Self-Similarity in General Relativity \endtitle
• Perturbations and Critical Behavior in the Self-Similar Gravitational Collapse of a Massless Scalar Field
• Spatially self-similar spherically symmetric perfect-fluid models
• Timelike self-similar spherically symmetric perfect-fluid models

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• Critical phenomena in gravitational collapse (Physics Reports)
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• Theorems on existence and global dynamics for the Einstein equations
• Critical phenomena in gravitational collapse - Living Reviews
• On dynamical systems approaches and methods in $f(R)$ cosmology
• A complete classification of spherically symmetric perfect fluid similarity solutions
• The Similarity Hypothesis in General Relativity
• Can a primordial black hole or wormhole grow as fast as the universe?
• Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity
• Stability criterion for self-similar solutions with perfect fluids in general relativity
• Spacetime structure of self-similar spherically symmetric perfect fluid solutions
• On Physical Properties of Cylindrically Symmetric Self-Similar Solutions
• Cosmological global dynamical systems analysis
• Kinematic Self-Similar Plane Symmetric Solutions
• Stability analysis of self-similar behaviors in perfect fluid gravitational collapse
• Breakdown of self-similar evolution in homogeneous perfect fluid collapse
• Critical collapse of a massive scalar field in semi-classical loop quantum gravity