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

Abstract We investigate mass ladder operators for the static BTZ-like black hole in Einstein-bumblebee gravity and probe the quasinormal frequencies of the mapped modes using mass ladder operators for a scalar perturbation under Dirichlet and Neumann boundary conditions. We find 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 in the Lorentz symmetry breaking parameter under the two boundary conditions. Note that, under the Neumann boundary condition, the mapped modes caused by the mass ladder operator are unstable. Moreover, the mass ladder operators do not change the Breitenlohner-Freedman bound for the scalar modes, as in the case of the usual BTZ black hole. These results could aid us in further understanding the conformal symmetry and Lorentz symmetry breaking in Einstein-bumblebee gravity.