Advances in Mathematical Physics
Volume 2012 (2012), Article ID 281705, 42 pages
Review Article

A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method

1Department of Physics, Tamkang University, Tamsui, New Taipei City 25137, Taiwan
2National Institute for Theoretical Physics, School of Physics, University of the Witwatersrand, Wits 2050, South Africa
3Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
4International College and Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan

Received 18 November 2011; Revised 12 March 2012; Accepted 15 March 2012

Academic Editor: Ricardo Weder

Copyright © 2012 H. T. Cho et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We discuss how to obtain black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second-order ordinary differential equations. We introduce the standard version of this method and present an improvement more suitable for numerical implementation. We demonstrate that the AIM can be used to find radial QNMs for Schwarzschild, Reissner-Nordström (RN), and Kerr black holes in a unified way. We discuss some advantages of the AIM over the continued fractions method (CFM). This paper presents for the first time the spin 0, 1/2 and 2 QNMs of a Kerr black hole and the gravitational and electromagnetic QNMs of the RN black hole calculated via the AIM and confirms results previously obtained using the CFM. We also present some new results comparing the AIM to the WKB method. Finally we emphasize that the AIM is well suited to higher-dimensional generalizations and we give an example of doubly rotating black holes.