2 research outputs found
On the stability of scalar-vacuum space-times
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".Comment: 18 pages, 5 figures. A few comments and references added. Final
version accepted at EPJ
Scalar wormholes with nonminimal derivative coupling
We consider static spherically symmetric wormhole configurations in a
gravitational theory of a scalar field with a potential and
nonminimal derivative coupling to the curvature describing by the term
in the
action. We show that the flare-out conditions providing the geometry of a
wormhole throat could fulfilled both if (phantom scalar) and
(ordinary scalar). Supposing additionally a traversability, we
construct numerical solutions describing traversable wormholes in the model
with arbitrary , and (no potential). The
traversability assumes that the wormhole possesses two asymptotically flat
regions with corresponding Schwarzschild masses. We find that asymptotical
masses of a wormhole with nonminimal derivative coupling could be positive
and/or negative depending on . In particular, both masses are positive
only provided , otherwise one or both wormhole masses are
negative. In conclusion, we give qualitative arguments that a wormhole
configuration with positive masses could be stable.Comment: 17 pages, 8 figure