Singularity Structure and Stability Analysis of the Dirac Equation on the Boundary of the Nutku Helicoid Solution
arXiv:0711.0612 · doi:10.1063/1.2913520
Abstract
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.
Version to appear in JMP
References in corpus (14)
- On reducing the Heun equation to the hypergeometric equation
- The 192 Solutions of the Heun Equation
- Exact Solutions of Regge-Wheeler Equation and Quasi-Normal Modes of Compact Objects
- Low-temperature asymptotics of integrable systems in an external field
- Toric Sasaki-Einstein manifolds and Heun equations
- Heun equation, Teukolsky equation, and type-D metrics
- Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces
- Ince's limits for confluent and double-confluent Heun equations
- The generalized Heun equation in QFT in curved space-times
- On polynomial solutions of Heun equation
- On quasi-normal modes and the AdS_5/CFT_4 correspondence
- Dirac Equation in the Background of the Nutku Helicoid Metric
- Absorption Cross Section of Scalar Field in Supergravity Background
- Gravitational Instantons from Minimal Surfaces
Cited by in corpus (6)
- Heun-type solutions for Schwarzschild metric with electromagnetic fields
- Quantum Field Theory Applications of Heun Type Functions
- Exact helicoidal and catenoidal solutions in Einstein-Maxwell theory
- Quantized Black Hole and Heun function
- Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field
- Analysis of scalar fields with series convolution