Quasinormal modes of the spherical bumblebee black holes with a global monopole

The bumblebee model is an extension of the Einstein-Maxwell theory that allows for the spontaneous breaking of the Lorentz symmetry of the spacetime. In this paper, we study the quasinormal modes of the spherical black holes in this model that are characterized by a global monopole. We analyze the two cases with a vanishing cosmological constant or a negative one (the anti-de Sitter case). We find that the black holes are stable under the perturbation of a massless scalar field. However, both the Lorentz symmetry breaking and the global monopole have notable impacts on the evolution of the perturbation. The Lorentz symmetry breaking may prolong or shorten the decay of the perturbation according to the sign of the breaking parameter. The global monopole, on the other hand, has different effects depending on whether a nonzero cosmological constant presences: it reduces the damping of the perturbations for the case with a vanishing cosmological constant, but has little influence for the anti-de Sitter case.