Quantum effects in Reissner-Nordstr\"{o}m black hole surrounded by magnetic field: the scalar wave case

We study the interaction between a massless scalar fields and the spacetime generated by charged black hole surrounded by magnetic field. The equations of motion are written into a Heun form, and its analytical solutions are obtained. These solutions have an explicit dependence on the parameter of the magnetic field. We obtain the exact Hawking radiation spectrum, the regular partial wave scattering, and the resonant frequencies (quasispectrum) expression. The special case of a Schwarzschild black hole surrounded by magnetic field is analyzed and the solutions are shown.