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Journal of Mathematical Physics / Volume 53 / Issue 2 / ARTICLES / General Relativity and Gravitation

J. Math. Phys. 53, 022503 (2012); http://dx.doi.org/10.1063/1.3682273 (4 pages)

Asymptotic stability of vacuum twisting type II metrics

Włodzimierz Natorf

Department of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Prague 8, Czech Republic

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(Received 18 October 2011; accepted 16 January 2012; published online 7 February 2012)

We generalize the result of Lukács et al. on asymptotic stability of the Schwarzschild metric with respect to perturbations in the Robinson-Trautman class of metrics to the case of Petrov type II twisting metrics, under the condition of asymptotic flatness at future null infinity. The Bondi energy is used as the Lyapunov functional and we prove that the “final state” of such metrics is the Kerr metric.

© 2012 American Institute of Physics

Article Outline

  1. CONVENTIONS AND NOTATION
  2. INTRODUCTION
  3. “NON-RADIATING” TYPE II METRICS
    1. I = 0, L , u transformable to 0
    2. I = 0, L , u not transformable to 0
  4. SUMMARY

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KEYWORDS and PACS

Keywords

asymptotic stability, black holes, Lyapunov methods, space-time configurations

PACS

  • 04.70.-s

    Physics of black holes

  • 04.20.Gz

    Spacetime topology, causal structure, spinor structure

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3682273

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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