Critical collapse of scalar fields beyond axisymmetry

  • James Healy
  • Pablo Laguna
Research Article


We investigate non-spherically symmetric, scalar field collapse of a family of initial data consisting of a spherically symmetric profile with a deformation proportional to the real part of the spherical harmonic \(Y_{21}(\theta ,\varphi )\). Independent of the strength of the anisotropy in the data, we find that supercritical collapse yields a black hole mass scaling \(M_h \propto (p-p^*)^\gamma \) with \(\gamma \approx 0.37\), a value remarkably close to the critical exponent obtained by Choptuik in his pioneering study in spherical symmetry. We also find hints of discrete self-similarity. However, the collapse experiments are not sufficiently close to the critical solution to unequivocally claim that the detected periodicity is from critical collapse echoing.


Black holes Numerical relativity Critical collapse 



We thank Matt Choptuik for helpful discussions and comments. Work supported by NSF grants 0653443, 0855892, 0914553, 0941417, 0903973, 0955825. Computations at Teragrid TG-PHY120016 and Georgia Tech FoRCE cluster. JH gratefully acknowledges the NSF for financial support from Grants PHY-1305730 and PHY-0969855.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Center for Relativistic Astrophysics and School of PhysicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Center for Computational Relativity and Gravitation, School of Mathematical SciencesRochester Institute of TechnologyRochesterUSA

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