Scalar perturbation around rotating Einstein-bumblebee BTZ black holes under Robin boundary conditions: Quasinormal modes and superradiance

We investigate the scalar perturbation around a rotating Einstein-bumblebee BTZ black hole under Robin boundary conditions. It is shown that the relationship curves between real and imaginary parts of scalar quasinormal modes in the complex plane depend on the black hole spin parameter j and the Lorentz symmetry breaking parameter s. The shapes of these curves are similar for different s, but heavily depend on the spin parameter j. With the increase of j, the symmetry of these curves with respect to the imaginary axis in the complex plane is gradually broken for different s. We also discuss the energy and angular momentum fluxes across the black hole horizon under Robin boundary conditions, and probe the changes of the threshold parameter related to the superradiance in Robin boundary conditions with the symmetry breaking parameter and the spin parameter. The combination of the Lorentz symmetry violation and the Robin boundary condition provides richer physics in the scalar perturbation around a rotating Einstein-bumblebee BTZ black hole.