Degenerate rotating black holes, chiral CFTs and Fermi surfaces I — Analytic results for quasinormal modes
Abstract
In this work we discuss charged rotating black holes in AdS _{5} × S ^{5} that degenerate to extremal black holes with zero entropy. These black holes have scaling properties between charge and angular momentum similar to those of Fermi surface operators in a subsector of {N} = 4 SYM. We add a massless uncharged scalar to the five dimensional supergravity theory, such that it still forms a consistent truncation of the type IIB ten dimensional supergravity and analyze its quasinormal modes. Separating the equation of motion to a radial and angular part, we proceed to solve the radial equation using a matched asymptotic expansion method applied to Heun's equation with two nearby singularities. We use the continued fraction method for the angular Heun equation and obtain numerical results for the quasinormal modes. In the case of the nearsupersymmetric black hole we present some analytic results for the decay rates of the scalar perturbations. The spectrum of quasinormal modes obtained is similar to that of a chiral 1 + 1 CFT, which is consistent with the conjectured fieldtheoretic dual. In addition, some of the modes can be found analytically.
 Publication:

Journal of High Energy Physics
 Pub Date:
 August 2012
 DOI:
 10.1007/JHEP08(2012)109
 arXiv:
 arXiv:1206.3735
 Bibcode:
 2012JHEP...08..109B
 Keywords:

 AdSCFT Correspondence;
 Black Holes;
 Spacetime Singularities;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 41 pages, 1 figure, LaTeX