Quasinormal modes for massless topological black holes

TL;DR

This work derives exact analytic quasinormal modes for a massive scalar field nonminimally coupled to curvature on massless topological AdS black holes with negatively curved horizons. By solving the Klein–Gordon equation and enforcing ingoing behavior at the horizon together with vanishing energy flux at infinity, the authors obtain closed-form frequencies in four and higher dimensions, revealing two mode families tied to the effective mass $m_{ extrm{eff}}^{2}$ and the transverse spectrum. The results establish Breitenlohner–Freedman type bounds ensuring stability, show damping rates that are independent of the transverse eigenvalue $\xi$, and extend to arbitrary $d$ with explicit frequency formulas $\omega = \pm \xi - i\left(2n+1\pm\sqrt{\left(\frac{d-1}{2}\right)^{2}+m_{ extrm{eff}}^{2}l^{2}}\right)$. These analytic expressions illuminate the AdS/CFT interpretation by linking $\mathrm{Im}(\omega)$ to the relaxation time of boundary thermal states and clarify the role of the correct Laplacian spectrum on the topological horizon in stability analyses.

Abstract

An exact expression for the quasinormal modes of scalar perturbations on a massless topological black hole in four and higher dimensions is presented. The massive scalar field is nonminimally coupled to the curvature, and the horizon geometry is assumed to have a negative constant curvature.