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We study torsional oscillations of neutron stars in the scalar-tensor theoryof gravity using the relativistic Cowling approximation. We compute unperturbedneutron star models adopting realistic equations of state for the neutronstar's core and crust. For scalar-tensor theories that allow for spontaneousscalarization, the crust thickness can be significantly smaller than in generalrelativity. We derive the perturbation equation describing torsionaloscillations in scalar-tensor theory, and we solve the corresponding eigenvalueproblem to find the oscillation frequencies. The fundamental mode (overtone)frequencies become smaller (larger) than in general relativity for scalarizedstellar models. Torsional oscillation frequencies may yield information on thecrust microphysics if microphysics effects are not degenerate withstrong-gravity effects, such as those due to scalarization. To address thisissue, we consider two different models for the equation of state of the crustand we look at the effects of electron screening. The effect of scalarizationon torsional oscillation frequencies turns out to be smaller than uncertaintiesin the microphysics for all spontaneous scalarization models allowed by binarypulsar observations. Our study shows that the observation of quasi-periodicoscillations (QPOs) following giant flares can be used to constrain themicrophysics of neutron star crusts, whether spontaneous scalarization occursor not.

Torsional oscillations of neutron stars in scalar-tensor theory of gravity