Tsutomu Kobayashi, Hayato Motohashi, Teruaki Suyama
We perform a fully relativistic analysis of odd-type linear perturbations
around a static and spherically symmetric solution in the most general
scalar-tensor theory with second-order field equations. It is shown that, as in
the case of general relativity, the quadratic action for the perturbations
reduces to the one having only a single dynamical variable, from which concise
formulas for no-ghost and no-gradient instability conditions are derived. Our
result is applicable to all the theories of gravity with an extra scalar degree
of freedom. We demonstrate how the generic formulas can be applied to some
particular examples such as the Brans-Dicke theory, $f(R)$ models, and Galileon
gravity.
View original:
http://arxiv.org/abs/1202.4893
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