Relativistic Correction to the r-mode Frequency in Light of Multimessenger Constraints

R-mode oscillations of rotating neutron stars are promising candidates for continuous gravitational wave (GW) observations. The r-mode frequencies slowly Newtonian well-known and independent the equation state (EOS) but stars, several mechanisms can alter frequency which relativistic correction is dominant relevant most stars. sensitive searches GWs those known pulsars GW in targeted narrow bands few Hz. In this study, we investigate effect state-of-the-art multi-messenger constraints on relativistic, rotating, barotropic Imposing these recent EOS, find that range slightly higher from previous study band increase upto 8-25% candidate PSR J0537-6910 depending compactness. We also derive universal relations between dimensionless tidal deformability be used to estimate dynamical tide resonant excitation during inspiral signal. These results construct parameter space data constrain nuclear following a successful detection.