Critical exponents of extremal Kerr perturbations

Samuel E. Gralla, Peter Zimmerman

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We show that scalar, electromagnetic, and gravitational perturbations of extremal Kerr black holes are asymptotically self-similar under the near-horizon, late-time scaling symmetry of the background metric. This accounts for the Aretakis instability (growth of transverse derivatives) as a critical phenomenon associated with the emergent symmetry. We compute the critical exponent of each mode, which is equivalent to its decay rate. It follows from symmetry arguments that, despite the growth of transverse derivatives, all generally covariant scalar quantities decay to zero.

Original languageEnglish (US)
Article number095002
JournalClassical and Quantum Gravity
Issue number9
StatePublished - Mar 19 2018


  • critical exponents
  • extremal Kerr
  • perturbations

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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