Abstract
Continuously self-similar (CSS) solutions for the gravitational collapse of a spherically symmetric perfect fluid, with the equation of state with a constant, are constructed numerically and their linear perturbations, both spherical and nonspherical, are investigated. The axial perturbations admit an analytical treatment. All others are studied numerically. For intermediate equations of state, with the CSS solution has one spherical growing mode, but no nonspherical growing modes. That suggests that it is a critical solution even in (slightly) nonspherical collapse. For this range of we predict the critical exponent for the black hole angular momentum to be times the critical exponent for the black hole mass. For this gives an angular momentum critical exponent of correcting a previous result. For stiff equations of state, the CSS solution has one spherical and several nonspherical growing modes. For soft equations of state, the CSS solution has growing modes: a spherical one, and an axial mode (with
- Received 9 October 2001
DOI:https://doi.org/10.1103/PhysRevD.65.084021
©2002 American Physical Society