Decay Of Scalar Fields In A Stationary Axisymmetric EMDA Black Hole Geometry

Superstring theory springing up in recent years is still the only known self-consistent theory which can quantize the gravity and unify the gravity, the electromagnetic interaction, the weak interaction and the strong interaction. This theory can explain the cosmic genesis and evolution, and figure out the problems of modern physics. In terms of the dilaton spacetimes in string theory, it has qualitatively different properties from those appearing in general relativity because of the apear-ance of dilaton. So there have been many investigations concerning the spacetimes of dilaton black hole. But people only discuss the evolution of perturbations in the static, spherically symmetric black hole geometry up to the present because of the complexity. Thus, it is worthwhile to investigate the decay of scalar fields in the background of dilaton black hole being the stationary axisymmetric solution of the so-called low-energy string theory. We will study the scalar late-time tails and quasinormal modes (QNMs) in this considered black hole.We investigate analytically the late-time tails of massless and massive scalar fields in a stationary axisymmetric Einstein-Maxwell dilaton-axion (EMDA) black hole geometry using the black-hole Green's function with the spectral decomposition method. It is shown that the asymptotic behavior of massless perturbations is dominated by the inverse power-law decaying tail t^-(2l+3), and the intermediate asymptotic behavior of massive perturbations is dominated by the oscillatory inverse power-law decaying tail t^-(l+3/2) sin(μt), but at asymptotically late times by the asymptotic tail t^-5/6 sin(μt) which may be a quite general feature for the evolution of massive scalar fields in any four-dimensional asymptotically flat rotating black hole geometry.We also calculated numerically the massless scalar QNMs of this EMDA black hole using the continued fraction method first proposed by Leaver. We obtain the slowly damped QNMs (fundamental quasinormal frequencies) and study the peculiar behaviors of them. The main conclusions and their physical implications are the following: (1) The massless scalar fundamental quasinormal frequencies of the EMDA black hole are affected by the dilaton parameter D, the rotational parameter a, the multiple moment / and the azimuthal number m. (2) If a, l and m are fixed,...