Advertisement

Critical collapse of scalar fields beyond axisymmetry

  • James Healy
  • Pablo Laguna
Research Article

Abstract

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.

Keywords

Black holes Numerical relativity Critical collapse 

Notes

Acknowledgments

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.

References

  1. 1.
    Abrahams, A.M., Evans, C.R.: Critical behavior and scaling in vacuum axisymmetric gravitational collapse. Phys. Rev. Lett. 70, 2980–2983 (1993). doi: 10.1103/PhysRevLett.70.2980 Google Scholar
  2. 2.
    Baker, J.G., Centrella, J., Choi, D.I., Koppitz, M., van Meter, J.: Gravitational-wave extraction from an inspiraling configuration of merging black holes. Phys. Rev. Lett. 96(11), 111 (2006). doi: 10.1103/PhysRevLett.96.111102 Google Scholar
  3. 3.
    Bode, T., Haas, R., Bogdanovic, T., Laguna, P., Shoemaker, D.: Relativistic mergers of supermassive black holes and their electromagnetic signatures. Astrophys. J. 715, 1117–1131 (2010). doi: 10.1088/0004-637X/715/2/1117 ADSCrossRefGoogle Scholar
  4. 4.
    Campanelli, M., Lousto, C.O., Marronetti, P., Zlochower, Y.: Accurate evolutions of orbiting black-hole binaries without excision. Phys. Rev. Lett. 96(11), 111 (2006). doi: 10.1103/PhysRevLett.96.111101 Google Scholar
  5. 5.
    Choptuik, M.W.: Universality and scaling in gravitational collapse of a massless scalar field. Phys. Rev. Lett. 70, 9–12 (1993). doi: 10.1103/PhysRevLett.70.9 Google Scholar
  6. 6.
    Choptuik, M.W., Hirschmann, E.W., Liebling, S.L., Pretorius, F.: Critical collapse of the massless scalar field in axisymmetry. Phys. Rev. D 68(4), 044007 (2003). doi: 10.1103/PhysRevD.68.044007 ADSCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gundlach, C., Martín-García, J.M.: Critical phenomena in gravitational collapse. Living Rev. Relat. 10, 5 (2007)ADSGoogle Scholar
  8. 8.
    Hilditch, D., Baumgarte, T.W., Weyhausen, A., Dietrich, T., Brügmann, B., Montero, P.J., Müller, E.: Collapse of nonlinear gravitational waves in moving-puncture coordinates. Phys. Rev. D 88(10), 103009 (2013). doi: 10.1103/PhysRevD.88.103009 ADSCrossRefGoogle Scholar
  9. 9.
    Husa, S., Hinder, I., Lechner, C.: Kranc: a mathematica application to generate numerical codes for tensorial evolution equations. Comput. Phys. Commun. 174, 983–1004 (2006)ADSCrossRefMATHGoogle Scholar
  10. 10.
    Löffler, F., Faber, J., Bentivegna, E., Bode, T., Diener, P., Haas, R., Hinder, I., Mundim, B.C., Ott, C.D., Schnetter, E., Allen, G., Campanelli, M., Laguna, P.: The Einstein toolkit: a community computational infrastructure for relativistic astrophysics. ArXiv e-prints (2011)Google Scholar
  11. 11.
    Martín-García, J.M., Gundlach, C.: All nonspherical perturbations of the Choptuik spacetime decay. Phys. Rev. D 59(6), 064031 (1999). doi: 10.1103/PhysRevD.59.064031 ADSCrossRefMathSciNetGoogle Scholar
  12. 12.
    Olabarrieta, I., Ventrella, J.F., Choptuik, M.W., Unruh, W.G.: Critical behavior in the gravitational collapse of a scalar field with angular momentum in spherical symmetry. Phys. Rev. D 76(12), 124014 (2007). doi: 10.1103/PhysRevD.76.124014 ADSCrossRefGoogle Scholar
  13. 13.
    Sorkin, E.: On critical collapse of gravitational waves. Class. Quantum Gravity 28(2), 025,011 (2011). doi: 10.1088/0264-9381/28/2/025011 CrossRefMathSciNetGoogle Scholar

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

Personalised recommendations