Stability Analysis of Canonical Acoustic Black Hole

Abstract

In this paper, we investigate the stability of canonical acoustic black hole under the perturbation of non-minimally coupling scalar field, electromagnetic field and Dirac field. The quasi-normal modes(QNMs) are computed using the three-order WKB approximation method. The results show that, for all these three kinds of perturbation, the values of the effective potential are positive, while the imaginary parts of QNMs are negative, the canonical acoustic black hole is a table. In details respectively, for scalar field perturbation, the effective potential and the QNMs depend on the angular quantum number $l$, the overtone number $n$, and the coupling parameter ζ, the perturbation decays more rapidly for bigger ζ. For electromagnetic field perturbation, the effective potential and QNMs depend on $l$ and $n$. For Dirac field perturbation, the effective potential and QNMs depend on $n$ and the total angular quantum number | k |.