Analytic solutions in the dyon black hole with a cosmic string: Scalar fields, Hawking radiation and energy flux

• A cosmic string is introduced along the axis of symmetry of the dyonic black hole.
• The covariant Klein–Gordon equation for a charged massive scalar field in this background is analyzed.
• Both angular and radial parts are transformed to a confluent Heun equation.
• The resulting Hawking radiation spectrum and the energy flux are obtained.

Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein–Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux.