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The Quasi-normal Modes of Charged Scalar Fields in Kerr-Newman black hole and Its Geometric Interpretation

It is well-known that there is a geometric correspondence between high-frequency quasi-normal modes (QNMs) and null geodesics (spherical photon orbits). In this paper, we generalize such correspondence to charged scalar field in Kerr-Newman space-time. In our case, the particle and black hole are all charged, so one should consider non-geodesic orbits. Using the WKB approximation, we find that the real part of quasi-normal frequency corresponds to the orbits frequency, the imaginary part of the frequency corresponds to the Lyapunov exponent of these orbits and the eigenvalue of angular equation corresponds to carter constant. From the properties of the imaginary part of quasi-normal frequency of charged massless scalar field, we can still find that the QNMs of charged massless scalar field possess the zero damping modes in extreme Kerr-Newman spacetime under certain condition which has been fixed in this paper.