Renormalization group approach to Einstein-Rosen waves

Tomohiro Harada and Sanjay Jhingan
Phys. Rev. D 87, 064043 – Published 28 March 2013

Abstract

We present a renormalization group analysis to Einstein-Rosen waves or vacuum spacetimes with whole-cylinder symmetry. It is found that self-similar solutions appear as fixed points in the renormalization group transformation. These solutions correspond to the explosive gravitational waves and the collapsing gravitational waves at late times and early times, respectively. Based on the linear perturbation analysis of the self-similar solutions, we conclude that the self-similar evolution is stable as explosive gravitational waves under the condition of no incoming waves, while it is weakly unstable as collapsing gravitational waves. The result implies that self-similar solutions can describe the asymptotic behavior of more general solutions for exploding gravitational waves and thus extends the similarity hypothesis in general relativity from spherical symmetry to cylindrical symmetry.

  • Figure
  • Received 21 February 2013

DOI:https://doi.org/10.1103/PhysRevD.87.064043

© 2013 American Physical Society

Authors & Affiliations

Tomohiro Harada1,* and Sanjay Jhingan2,†

  • 1Department of Physics, Rikkyo University, Toshima, Tokyo 171-8501, Japan
  • 2Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi 110025, India

  • *harada@rikkyo.ac.jp
  • sanjay.jhingan@gmail.com

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Vol. 87, Iss. 6 — 15 March 2013

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