Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity

Abstract

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state $P=\rho$. A wide class of self-similar solutions turn out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solution for the spherical collapse of a stiff fluid if we allow sufficiently small discontinuity in the density gradient field in the initial data sets. The self-similar scalar-field solution, which was recently found numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19} 6359), is also unstable. Both the flat Friedmann universe with a scalar field and that with a stiff fluid suffer from kink instability at the particle horizon scale.

15 pages, accepted for publication in Classical and Quantum Gravity, typos corrected

References in corpus (6)

• Critical phenomena in gravitational collapse (Physics Reports)
• Convergence to a self-similar solution in general relativistic gravitational collapse
• Black-hole threshold solutions in stiff fluid collapse
• Stability criterion for self-similar solutions with perfect fluids in general relativity
• Critical phenomena in Newtonian gravity
• Criticality and convergence in Newtonian collapse

Cited by in corpus (13)

• The Similarity Hypothesis in General Relativity
• Non-existence of self-similar solutions containing a black hole in a universe with a stiff fluid or scalar field or quintessence
• Novel Cauchy-horizon instability
• Attractors of Hamilton nonlinear partial differential equations
• Simple analytic model of wormhole formation
• On the global visibility of a singularity in spherically symmetric gravitational collapse
• Inside charged black holes I. Baryons
• Unveiling horizons in quantum critical collapse
• Kink instability and stabilization of the Friedmann universe with scalar fields
• Kink Stability of Isothermal Spherical Self-Similar Flow Revisited
• Self-similar motion of a Nambu-Goto string
• Kink Stability of Self-Similar Solutions of Scalar Field in 2+1 Gravity
• Perturbation theory of spherically symmetric self-similar black holes