Quasi-normal modes, area spectra and multi-horizon spacetimes

We suggest an interpretation for the highly damped QNM frequencies of the spherically symmetric multi-horizon spacetimes (Reissner-Nordström, Schwarzschild-deSitter, Reissner-Nordström-deSitter) following Maggiore’s proposal about the link between the asymptotic QNM frequencies and the black hole thermodynamics. We show that the behavior of the asymptotic frequencies is easy to understand if one assumes that all of the horizons have the same equispaced area spectra. The QNM analysis is then consistent with the choice of the area spectra to be the one originally proposed for the black hole’s horizon by Bekenstein: A = 8πn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \left( {l_p^2 = {1}} \right) $\end{document}. The interpretation of the highly damped QNM frequencies in the multi-horizon case is based on the similar grounds as in the single horizon (Schwarzschild) case, but it has some new features that are discussed in the paper.