Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field

We study a charged and massive scalar field in the background of Nutku-Ghezelbash-Kumar metric which is obtained by addition time coordinate to Nutku helicoid non-trivial way. The angular part Klein-Gordon equation can be written as double confluent Heun equation. radial cannot solved terms known function its general form. However, some special cases, also explicitly full numerically observe that electromagnetic parameter defines an effective cut-off on range coordinate. Finally, we obtain quasi-exact solution with approximation.