Polar Quasinormal Modes of Neutron Stars in Massive Scalar-Tensor Theories

We study polar quasinormal modes of relativistic stars in scalar-tensor theories, where we include a massive gravitational scalar field and employ the standard Brans-Dicke coupling function. For potential consider simple mass term as well associated with $R^2$ gravity. The presence makes spectrum much richer than General Relativity. here investigate radial ($l=0$) quadrupole ($l=2$). general $l=0$ normal turn into that are able to propagate outside stars. In addition pressure-led new scalar-led $\phi$-modes arise. analyze dependence mode frequencies decay times on mass.