Asymptotic quasinormal modes of a coupled scalar field in the Gibbons-Maeda dilaton spacetime

Abstract

Adopting the monodromy technique devised by Motl and Neitzke, we investigate analytically the asymptotic quasinormal frequencies of a coupled scalar field in the Gibbons-Maeda dilaton spacetime. We find that it is described by $e^{\beta \omega }=-[1+2\cos (\frac{\sqrt{2\xi +1}}{2}\pi )]-e^{-{\beta }_I\omega }[2+2\cos (\frac{\sqrt{2\xi +1}}{2}\pi )]$, which depends on the structure parameters of the background spacetime and on the coupling between the scalar and gravitational fields. As the parameters $\xi$ and ${\beta }_I$ tend to zero, the real parts of the asymptotic quasinormal frequencies becomes $T_H\ln 3$, which is consistent with Hod's conjecture. When $\xi =91/18$, the formula becomes that of the Reissner-Nordström spacetime.

6 pages, 1 figure

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