Properties of scalar wave emission in a scalar-tensor theory with kinetic screening

We study numerically the scalar wave emission by a non-spherical oscillation of neutron stars in a scalar-tensor theory of gravity with kinetic screening, considering both the monopole and quadrupole mode emission. In agreement with previous results in the literature, we find that the monopole is always suppressed by the screening effect, regardless of the size of the screening radius, $r_{\rm sc}$. For the quadrupole mode, however, our analysis shows that the suppression only occurs for screening radius larger than the wavelength of scalar waves, $\lambda_{\rm wave}$, but not for $r_{\rm sc} < \lambda_{\rm wave}$. This demonstrates that to fully understand the nature of this theory, it is necessary to study other more complex systems, such as neutron star binaries, considering a wide range of $r_{\rm sc}$ values.