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

Tomohiro Harada·Hideki Maeda
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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 $P=ρ$. 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.

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Tomohiro Harada, Hideki Maeda. 2003-12-01. Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity. https://doi.org/10.1088/0264-9381%2F21%2F2%2F003

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