On the stability of scalar-vacuum space-times
Sep, 2011
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Abstract: (arXiv)
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) = 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".Note:
- 18 pages, 5 figures. A few comments and references added. Final version accepted at EPJC
- field theory: scalar
- symmetry: rotation
- metric: perturbation
- solution: static
- space-time: vacuum state
- space-time: stability
- Einstein equation: solution
- phantom: scalar particle
- regularization
- wormhole: throat
References(38)
Figures(10)