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On the stability of spherically symmetric space-times in scalar-tensor gravity
We study the linear stability of vacuum static, spherically symmetric
solutions to the gravitational field equations of the
Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories (STT) of gravity,
restricting ourselves to nonphantom theories, massless scalar fields and
configurations with positive Schwarzschild mass. We consider only small radial
(monopole) perturbations as the ones most likely to cause an instability. The
problem reduces to the same Schroedinger-like master equation as is known for
perturbations of Fisher's solution of general relativity (GR), but the
corresponding boundary conditions that affect the final result of the study
depend on the choice of the STT and a particular solution within it. The
stability or instability conclusions are obtained for the Brans-Dicke, Barker
and Schwinger STT as well as for GR nonminimally coupled to a scalar field with
an arbitrary parameter .Comment: 16 pages, 4 figures, each of 2 part