Quasinormal modes of Dirac field in 2 + 1 dimensional gravitational wave background

In this study, we investigate the solutions of the massive and massless Dirac equation, at first, in the $2+1$ dimensional gravitational wave background and then in the background with the presence of a constant magnetic field. In both situations, using the solutions obtained in terms of the confluent Heun functions, we calculate the quasinormal modes (QNMs) and discuss the stability conditions of the background. Comparing the quality factors derived from the QNMs in the existence of Dirac field mass and constant magnetic field with together, we see that the magnetic field plays a very important role in reducing the number of the gravitational wave oscillations because of its damping or screening effect, but there is no magnetic field effect on the proper oscillations of the gravitational wave. In addition, we acquire quasi-resonance modes (QRMs) for the massive test field in the absence of magnetic field and massless Dirac field in the presence of magnetic field from these QNMs. In both situations, the gravitational wave (GW) background becomes a good oscillator because the quality factor is very high. Moreover, we discuss the gravitational redshift for the wave background. Finally, we see that the obtained the GW frequencies and redshift values in the context of the study are compatible with the observational data.