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On the stability of scalar-vacuum space-times

  • K. A. BronnikovEmail author
  • J. C. Fabris
  • A. Zhidenko
Regular Article - Theoretical Physics

Abstract

We study the stability of static, spherically symmetric solutions to the Einstein equations with a scalar field as the source. We describe a general methodology of studying small radial perturbations of scalar-vacuum configurations with arbitrary potentials V(ϕ), and in particular space-times with throats (including wormholes), which are possible if the scalar is phantom. At such a throat, the effective potential for perturbations V eff has a positive pole (a potential wall) that prevents a complete perturbation analysis. We show that, generically, (i) V eff has precisely the form required for regularization by the known S-deformation method, and (ii) a solution with the regularized potential leads to regular scalar field and metric perturbations of the initial configuration. The well-known conformal mappings make these results also applicable to scalar-tensor and f(R) theories of gravity. As a particular example, we prove the instability of all static solutions with both normal and phantom scalars and V(ϕ)≡0 under spherical perturbations. We thus confirm the previous results on the unstable nature of anti-Fisher wormholes and Fisher’s singular solution and prove the instability of other branches of these solutions including the anti-Fisher “cold black holes.”

Keywords

Dark Energy Conformal Factor Einstein Frame Wormhole Solution Throat Radius 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2011

Authors and Affiliations

  1. 1.Center for Gravitation and Fundamental MetrologyVNIIMSMoscowRussia
  2. 2.Institute of Gravitation and CosmologyPFURMoscowRussia
  3. 3.Departamento de FísicaUniversidade Federal do Espírito SantoVitóriaBrazil
  4. 4.Centro de Matemática, Computação e CogniçãoUniversidade Federal do ABCSanto AndréBrazil

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