Critical gravitational collapse of a perfect fluid: Nonspherical perturbations

Carsten Gundlach
Phys. Rev. D 65, 084021 – Published 29 March 2002
PDFExport Citation

Abstract

Continuously self-similar (CSS) solutions for the gravitational collapse of a spherically symmetric perfect fluid, with the equation of state p=κρ, with 0<κ<1 a constant, are constructed numerically and their linear perturbations, both spherical and nonspherical, are investigated. The l=1 axial perturbations admit an analytical treatment. All others are studied numerically. For intermediate equations of state, with 1/9<κ0.49, 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 κ we predict the critical exponent for the black hole angular momentum to be 5(1+3κ)/3(1+κ) times the critical exponent for the black hole mass. For κ=1/3 this gives an angular momentum critical exponent of μ0.898, correcting a previous result. For stiff equations of state, 0.49κ<1, the CSS solution has one spherical and several nonspherical growing modes. For soft equations of state, 0<κ<1/9, the CSS solution has 1+3 growing modes: a spherical one, and an l=1 axial mode (with m=1,0,1).

  • Received 9 October 2001

DOI:https://doi.org/10.1103/PhysRevD.65.084021

©2002 American Physical Society

Authors & Affiliations

Carsten Gundlach*

  • Enrico Fermi Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637
  • Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, United Kingdom

  • *Current address.

References (Subscription Required)

Click to Expand
Issue

Vol. 65, Iss. 8 — 15 April 2002

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×