Quasinormal modes for dynamical black holes

Realistic black holes are usually dynamical, noticeable, or sluggish. The Vaidya metric is a significant and tractable model for simulating a dynamical black hole. In this study, we consider scalar perturbations in a dynamical Vaidya black hole and explore the quasinoimal modes by employing the matrix method. We find the proper boundary conditions of the quasinormal modes from physical analysis in the background of a dynamical black hole for the first time. The results show that the eigenfrequencies become different at the apparent horizon and null infmity, because the physical interactions propagate with fmite velocity in nature. Any variation of the hole does not affect the boundary condition at null infinity in a fmite time. The quasinormal modes originated around the horizon would not immediately come down to, but slowly go to the final state following the mass accretion process of the hole. The precision of the matrix method is quite compelling, which reveals more details of the eigenfrequencies of the quasinormal mode of perturbations in the Vaidya spacetime.