Stability Analysis of Spherically Symmetric Star in Scalar-Tensor Theories of Gravity

A stability analysis of a spherically symmetric star in scalar-tensortheories of gravity is given in terms of the frequencies of quasi-normal modes.The scalar-tensor theories have a scalar field which is related to gravitation.There is an arbitrary function, the so-called coupling function, whichdetermines the strength of the coupling between the gravitational scalar fieldand matter. Instability is induced by the scalar field for some ranges of thevalue of the first derivative of the coupling function. This instability leadsto significant discrepancies with the results of binary-pulsar-timingexperiments and hence, by the stability analysis, we can exclude the ranges ofthe first derivative of the coupling function in which the instability sets in.In this article, the constraint on the first derivative of the couplingfunction from the stability of relativistic stars is found. Analysis in termsof the quasi-normal mode frequencies accounts for the parameter dependence ofthe wave form of the scalar gravitational waves emitted from theOppenheimer-Snyder collapse. The spontaneous scalarization is also discussed.Comment: 17 pages, including 6 eps figures. Accepted for publication in Progress of Theoretical Physics. Grammatical errors correcte