Mass ladder operators and quasinormal modes of the static BTZ-like black hole in the Einstein-bumblebee gravity

We investigate the mass ladder operators for the static BTZ-like black hole in the Einstein-bumblebee gravity, and probe the quasinormal frequencies of the mapped modes by the mass ladder operators for a scalar perturbation under the Dirichlet and Neumann boundary conditions. It is found that the mass ladder operators depend on the Lorentz symmetry breaking parameter, and the imaginary parts of the frequencies shifted by the mass ladder operators increase with the increase of the Lorentz symmetry breaking parameter under two boundary conditions. It should be noted that, under the Neumann boundary condition, the mapped modes caused by the mass ladder operator D0,k₊ are unstable. Moreover, the mass ladder operators do not change the Breitenlohner-Freedman bound for the scalar modes, just as in the usual BTZ black hole. These results could help us to further understand the conformal symmetry and Lorentz symmetry breaking in the Einstein-bumblebee gravity.