Quasinormal modes and late-time falloff of Finslerian black holes with cosmological constant

Abstract

Quasinormal modes of scalar and electromagnetic field perturbations in Finslerian Reissner-Nordstr\"om black holes with a cosmological constant are investigated in this paper. We analyze the fundamental frequencies and dynamical evolution of quasinormal modes using the WKB approximation and finite difference method, respectively. Both approaches show that the periods of oscillation of quasinormal modes increase with higher Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ if the multipole quantum number $l\ensuremath{\ge}2$. Using the Prony method, we show that the results obtained from the finite difference method are consistent with the results obtained from the WKB approximation. Quasinormal modes of Finslerian black holes possess spectrum splitting, which reflects the fact that the spherical symmetry of the Finslerian black holes is broken. The effects of the Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ on the late-time tails of scalar and electromagnetic field perturbations are shown. The late-time tails of the Finslerian Reissner-Nordstr\"om black holes possess a power-law falloff. The power-law index has a discontinuous jump, while the Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ varies from 0 to nonzero. Such a fact reflects the fact that asymptotic-infinity behaviors of the Finslerian Reissner-Nordstr\"om black holes are different from their counterparts in general relativity.