Quasi-normal modes of AdS black holes : A superpotential approach
T. R. Govindarajan, V. Suneeta
TL;DR
This work tackles the problem of computing quasi-normal modes (QNMs) of anti-de Sitter (AdS) black holes, focusing on AdS5-Schwarzschild backgrounds perturbed by a minimally coupled scalar field. It introduces a superpotential-inspired approach, motivated by exact BTZ results, to approximate the AdS QNM spectrum by representing the black-hole potential as a series derived from a superpotential and enforcing ingoing boundary conditions at the horizon and decay at infinity. The authors report a convergent procedure up to order N=18, finding that QNM frequencies scale with the surface gravity α for very small and very large black holes and with the horizon scale for large black holes, while highlighting a discrepancy with prior Horowitz–Hubeny calculations. These results provide a semi-analytic framework for AdS QNMs with potential implications for AdS/CFT thermalization and motivate extensions to charged and other-dimensional AdS black holes.
Abstract
A novel method, based on superpotentials is proposed for obtaining the quasi-normal modes of anti-de Sitter black holes. This is inspired by the case of the three-dimensional BTZ black hole, where the quasi-normal modes can be obtained exactly and are proportional to the surface gravity. Using this approach, the quasi-normal modes of the five dimensional Schwarzschild anti-deSitter black hole are computed numerically. The modes again seem to be proportional to the surface gravity for very small and very large black holes. They reflect the well-known instability of small black holes in anti-deSitter space.