Journal
EUROPEAN PHYSICAL JOURNAL C
Volume 71, Issue 11, Pages -Publisher
SPRINGER
DOI: 10.1140/epjc/s10052-011-1791-2
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Funding
- RFBR [09-02-00677a]
- NPK MU at PFUR
- FTsP Nauchnye i nauchnopedagogicheskie kadry innovatsionnoy Rossii
- Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq, Brazil)
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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(phi), 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(phi) equivalent to 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.
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