In some short gamma-ray bursts, precursor flares occurring ∼ seconds prior to the main episode have been observed. These flares may then be associated with the last few cycles of the inspiral when the orbital frequency is a few hundred Hz. During these final cycles, tidal forces can resonantly excite quasi-normal modes in the inspiralling stars, leading to a rapid increase in their amplitude. It has been shown that these modes can exert sufficiently strong strains onto the neutron star crust to instigate yieldings. Due to the typical frequencies of g-modes being ∼100Hz, their resonances with the orbital frequency match the precursor timings and warrant further investigation. Adopting realistic equations of state and solving the general-relativistic pulsation equations, we study g-mode resonances in coalescing quasi-circular binaries, where we consider various stellar rotation rates, degrees of stratification, and magnetic field structures. We show that for some combination of stellar parameters, the resonantly excited g1- and g2-modes may lead to crustal failure and trigger precursor flares.

The scalar tensor theory contains a coupling function connecting the quantities in the Jordan and Einstein frames, which is constrained to guarantee a transformation rule between frames. We simulate the supernovae core collapse with different choices of coupling functions defined over the viable region of the parameter space and find that a generic inverse-chirp feature of the gravitational waves in the scalar tensor scenario.

The scalar-tensor theory can be formulated in both Jordan and Einstein frames, which are conformally related together with a redefinition of the scalar field. As the solution to the equation of the scalar field in the Jordan frame does not have the one-to-one correspondence with that in the Einstein frame, we give a criterion along with some specific models to check if the scalar field in the Einstein frame is viable or not by confirming whether this field is reversible back to the Jordan frame. We further show that the criterion in the first parameterized post-Newtonian approximation can be determined by the parameters of the osculating approximation of the coupling function in the Einstein frame and can be treated as a viable constraint on any numerical study in the scalar-tensor scenario. We also demonstrate that the Brans-Dicke theory with an infinite constant parameter ω BD is a counterexample of the equivalence between two conformal frames due to the violation of the viable constraint.