Impact of the relativistic Cowling approximation on shear and interface modes of neutron stars

Neutron stars are amongst the most compact objects known in the universe, which, therefore, require General Relativity for an accurate description. Seismic excitations of these stars may encode information about their currently unknown internal composition. As General Relativity is a mathematically complex theory, such oscillations are often considered in the Cowling approximation in which the spacetime is assumed to be static. In this talk, we will focus on shear and interface modes of neutron stars related to an elastic crust and investigate the impact of the Cowling approximation; we find that its impact on shear modes is negligible, while interface modes seem to experience some modification. Furthermore, we extend a scheme based on properties of Breit-Wigner resonances that allows to estimate the damping times of slowly damped modes. The proposed scheme is numerically robust and we compare it to estimates employing the quadrupole formula.