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

TL;DR

This paper analytically derives the asymptotic quasinormal frequencies of a coupled scalar field in Gibbons-Maeda dilaton spacetime using monodromy techniques, revealing dependence on spacetime parameters and confirming Hod's conjecture.

Contribution

It provides a new analytical expression for quasinormal modes in dilaton spacetime, linking them to spacetime parameters and coupling, extending previous results to more general backgrounds.

Findings

Frequency formula depends on spacetime parameters and coupling.

Real parts approach $T_H \, \ln 3$ as parameters tend to zero.

Special case reproduces Reissner-Nordström spacetime results.

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-Nordstr\"{o}m spacetime.