Quasinormal modes of a scalar and an electromagnetic field in Finslerian-Schwarzschild spacetime

Quasinormal modes of scalar field and electromagnetic field in a specific Finslerian-Schwarzschild spacetime have been investigated in this paper. The equations of motion for scalar field and electromagnetic field have been constructed by Finslerian-Laplace operator and divergence operator. The solutions of the equations of motion are presented. The solutions of angular part for scalar field and electromagnetic field are different. The solutions of radial part are numerically analyzed via WKB approximation and finite difference method, which give the quasinormal frequencies and dynamic evolution of quasinormal modes, respectively. The spectrum splitting generated from spherical symmetry breaking of the Finslerian-Schwarzschild spacetime is shown. The analysis of the dynamical evolution of quasinormal modes shows that the Finslerian-Schwarzschild black hole is stable if the Finslerian parameter ε2 < 0.8.