Heun-type solutions for Schwarzschild metric with electromagnetic fields

We find confluent Heun solutions to the radial equations of two Halilsoy-Badawi metrics. For the first metric, we studied the radial part of the massless Dirac equation and for the second case, we studied the radial part of the massless Klein-Gordon equation.Comment: 8 pages, 2 figures. Matches the published versio

Heun and Mathieu functions as solutions of the Dirac equation

We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. While the Dirac equation written in the background of Nutku helicoid metric yields Mathieu functions as its solutions in four spacetime dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations. We must apply Atiyah-Patodi-Singer spectral boundary conditions to this system since the metric has a singularity at the origin.Comment: 5 pages, Prepared for the Spanish Relativity Meeting (ERE 2007), Tenerife, Spain, 10-14 Sep 200

An Exact Solution for Static Scalar Fields Coupled to Gravity in (2+1)(2+1)-Dimensions

We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.Comment: 9 pages. Replaced by a revised versio

Singularity Structure and Stability Analysis of the Dirac Equation on the Boundary of the Nutku Helicoid Solution

Dirac equation written on the boundary of the Nutku helicoid space consists of a system of ordinary differential equations. We tried to analyze this system and we found that it has a higher singularity than those of the Heun's equations which give the solutions of the Dirac equation in the bulk. We also lose an independent integral of motion on the boundary. This facts explain why we could not find the solution of the system on the boundary in terms of known functions. We make the stability analysis of the helicoid and catenoid cases and end up with an appendix which gives a new example where one encounters a form of the Heun equation.Comment: Version to appear in JM

Degenerate Rotating Black Holes, Chiral CFTs and Fermi Surfaces I - Analytic Results for Quasinormal Modes

In this work we discuss charged rotating black holes in $AdS_5 \times S^5$ 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 $\mathcal{N}=4$ 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 the asymptotic matching expansion method applied to a Heun 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 supersymmetric 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 field-theoretic dual. In addition, some of the modes can be found analytically.Comment: 41 pages, 1 figure, LaTeX; v2: typos corrected, references adde

General Hidden Conformal Symmetry of 4D Kerr-Newman and 5D Kerr Black Holes

There are two known CFT duals, namely the J-picture and the Q-picture, for a four-dimensional Kerr-Newman black hole, corresponding to the angular momentum $J$ and the electric charge $Q$ respectively. In our recent study we found a one-parameter class of CFT duals for extremal Kerr-Newman black hole, connecting these two pictures. In this paper we study these novel CFT duals for the generic non-extremal Kerr-Newman black hole. We investigate the hidden conformal symmetry in the low frequency scattering off Kerr-Newman black hole, from which the dual temperatures could be read. We find that there still exists a hidden conformal symmetry for a general CFT dual. We reproduce the correct Bekenstein-Hawking entropy from the Cardy formula, assuming the form of the central charge being invariant. Moreover we compute the retarded Green's function in the general CFT dual picture and find it is in good match with the CFT prediction. Furthermore we discuss the hidden conformal symmetries of the five dimensional Kerr black hole and obtain the similar evidence to support the general dual CFT pictures.Comment: 25 pages; Typos corrected; Revision in accordance to the changes in 1106.414