Probing tensor-vector-scalar theory with gravitational wave asteroseismology

In order to examine the gravitational waves emitted from the neutron stars in the tensor-vector-scalar (TeVeS) theory, we derive the perturbation equations for relativistic stars, where for simplicity we omit the perturbations of the vector field. That is, we consider the perturbations of scalar and tensor fields. With this assumption, we find that the axial gravitational waves, which are corresponding to the oscillations of spacetime (w modes), are independent from the perturbations of the scalar field and the effects of the scalar field can be mounted only via the background properties. Using two different equations of state, we calculate the complex eigenfrequencies of axial w modes and find that the dependences of frequencies on the stellar compactness are almost independent from the adopted equation of state and the parameter in TeVeS. Additionally, these dependences of frequencies of axial w modes in TeVeS are obviously different from those expected in general relativity. Thus the direct observations of gravitational waves could reveal the gravitational theory in the strong-field regime.